Practice Set 6.2 Algebra 10th Standard Maths Part 1 Chapter 6 Statistics Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 10 Maths Solutions covers the Practice Set 6.2 Algebra 10th Class Maths Part 1 Answers Solutions Chapter 6 Statistics.

10th Standard Maths 1 Practice Set 6.2 Chapter 6 Statistics Textbook Answers Maharashtra Board

Class 10 Maths Part 1 Practice Set 6.2 Chapter 6 Statistics Questions With Answers Maharashtra Board

Statistics Practice Set 6.2 Question 1.
The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 1
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 2
Cumulative frequency which is just greater than (or equal) to 500 is 650.
∴ The median class is 10 – 12.
Now, L = 10, f = 500, cf = 150, h = 2
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 3
∴ The median of the number of hours the workers work is 11.4 hours.

10th Class Algebra Practice Set 6.2 Question 2.
The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of data.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 4
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 5
Here, total frequency = ∑fi = N = 250
∴ \(\frac { N }{ 2 } \) = \(\frac { 250 }{ 2 } \) = 125
Cumulative frequency which is just greater than (or equal) to 125 is 153.
∴ The median class is 150 – 200.
Now, L = 150, f = 90, cf = 63, h = 50
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 6
∴ The median of the given data is 184 mangoes (approx).

Statistics Class 10 Practice Set 6.2 Question 3.
The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 7
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 8
Here, total frequency = ∑fi = N = 200
∴ \(\frac { N }{ 2 } \) = \(\frac { 200 }{ 2 } \) = 100
Cumulative frequency which is just greater than (or equal) to 100 is 184.
∴ The median class is 74.5 – 79.5.
Now, L = 74.5, f = 85, cf = 99, h = 5
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 9
∴ The median of the given data is 75 km/hr (approx.).

Practice Set 6.2 Geometry Class 10 Question 4.
The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 10
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 11
Cumulative frequency which is just greater than (or equal) to 52.5 is 67.
∴ The median class is 50 – 60.
Now, L = 50, f = 20, cf = 47, h = 10
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 12
∴ The median of the productions is 52750 bulbs (approx.).

Practice Set 6.2 Question 1.
If the number of scores is odd, then the (\(\frac { n+1 }{ 2 } \))th score is the median of the data. That is, the number of scores below as well as above \({ K }_{ \frac { n+1 }{ 2 } }\) is \(\frac { n-1 }{ 2 } \) Verify the fact by taking n = 2m + I. (Textbk pg. no. 139)
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 13
The sequence of the terms of scores is 1,2, 3, …….., m, m + 1, m + 2, …, 2m + 1
Thus, we have to prove that m + 1 is the middle term if the number of scores is 2m + 1
i.e. to prove
number of terms from 1 to m = number of terms from m + 2 to 2m + 1 …(i)
Consider the L.H.S. of equation (i)
The sequence is an A.P. with a = 1,d = 1, tn1 = m
tn1 = a + (n1 – 1) d
∴ m = 1 + (n1 – 1)1
∴ m = 1 + n1 – 1
∴ m = n1
Consider the R.H.S. of equation (ii)
The sequence is an A.P. with a = m + 2, d = 1, tn2 = 2m + 1
tn2 = a + (n2 – 1)d
∴ 2m + 1 = m + 2 + (n2 – 1)1
∴ 2m + 1 = m + n2 + 1
∴ m = n2
∴ number of terms from 1 to m = number of terms from m + 2 to 2m + 1 = m = \(\frac { n-1 }{ 2 } \)
∴ m + 1 is the middle term if the number of scores is 2m + 1.

Question 2.
If the number of the scores is even, then the mean of the middle two terms is the median. This is because the number of terms below \({ K }_{ \frac { n }{ 2 } }\) and above \({ K }_{ \frac { n+2 }{ 2 } }\) is equal, which is \(\frac { n-2 }{ 2 } \). Verify this by taking n = 2m. (Textbook pg. no. 139)
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.2 14
The sequence of the terms of scores is 1, 2, 3 … m – 1, m, m + 1, m + 2,…., 2m
Thus, we have to prove that m and m + 1 are the middlemost terms if the number of scores is 2m.
i.e. to prove
number of terms from 1 to m – 1 = number of terms from m + 2 to 2m …(i)
Consider the L.H.S. of equation (i)
The sequence is an A.P. with a = 1, d = 1, tn1 = m – 1
tn1 = a + (n1 – 1)d
∴ m – 1 = 1 + (n1 – 1)1
∴m – 1 = 1 + n1 – 1
∴ n1 = m – 1
Consider the R.H.S. of equation (i)
The sequence is an A.P. with a = m + 2, d = 1, tn2= 2m
tn2= a + (n2 – 1) d
∴ 2m = m + 2 + (n2 – 1)1
∴ 2m = m + 2 + n2 – 1
∴ n2 = m – 1
∴ number of terms from 1 to m – 1 = number of terms from m + 2 to 2m = m – 1 = \(\frac { n-2 }{ 2 } \)
∴ m and m + 1 are the middlemost terms if the number of scores is 2m.

Class 10 Maths Digest

Problem Set 5.1 Algebra 10th Standard Maths Part 1 Chapter 5 Probability Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 10 Maths Solutions covers the Problem Set 5 Algebra 10th Class Maths Part 1 Answers Solutions Chapter 5 Probability.

10th Standard Maths 1 Problem Set 5 Chapter 5 Probability Textbook Answers Maharashtra Board

Class 10 Maths Part 1 Problem Set 5 Chapter 5 Probability Questions With Answers Maharashtra Board

Question 1.
Choose the correct alternative answer for each of the following questions.

i. Which number cannot represent a probability?
(A) \(\frac { 2 }{ 3 } \)
(B) 1.5
(C) 15%
(D) 0.7
Answer:
The probability of any 0 to 1 or 0% to 100%. event is from
(B)

ii. A die is rolled. What is the probability that the number appearing on upper face is less than 3?
(A) \(\frac { 1 }{ 6 } \)
(B) \(\frac { 1 }{ 3 } \)
(C) \(\frac { 1 }{ 2 } \)
(D) 0
Answer:
(B)

iii. What is the probability of the event that a number chosen from 1 to 100 is a prime number?
(A) \(\frac { 1 }{ 5 } \)
(B) \(\frac { 6 }{ 25 } \)
(C) \(\frac { 1 }{ 4 } \)
(D) \(\frac { 13 }{ 50 } \)
Answer:
n(S) = 100
Let A be the event that the number chosen is a prime number.
∴ A = {2, 3, 5. , 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
∴ n(A) = 25
∴ P(A) = \(\frac { n(A) }{ n(S) } \) = \(\frac { 25 }{ 100 } \) = \(\frac { 1 }{ 4 } \)
(C)

iv. There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5?
(A) \(\frac { 1 }{ 5 } \)
(B) \(\frac { 3 }{ 5 } \)
(C) \(\frac { 4 }{ 5 } \)
(D) \(\frac { 1 }{ 3 } \)
Answer:
(A)

v. If n(A) = 2, P(A) = \(\frac { 1 }{ 5 } \), then n(S) = ?
(A) 10
(B) \(\frac { 5 }{ 2 } \)
(C) \(\frac { 2 }{ 5 } \)
(D) \(\frac { 1 }{ 3 } \)
Answer:
(A)

Question 2.
Basketball players John, Vasim, Akash were practising the ball drop in the basket. The probabilities of success for John, Vasim and Akash are \(\frac { 4 }{ 5 } \), 0.83 and 58% respectively. Who had the greatest probability of success ?
Solution:
The probability that the ball is dropped in the basket by John = \(\frac { 4 }{ 5 } \) = 0.80
The probability that the ball is dropped in the basket by Vasim = 0.83
The probability that the ball is dropped in the basket by Akash = 58% = \(\frac { 58 }{ 100 } \) = 0.58
0.83 > 0.80 > 0.58
∴ Vasim has the greatest probability of success.

Question 3.
In a hockey team there are 6 defenders , 4 offenders and 1 goalie. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that:
i. The goalie will be selected.
ii. A defender will be selected.
Solution:
Total number of players in the hockey team
= 6 + 4 + 1 = 11
∴ n(S) = 11

i. Let A be the event that the captain selected will be a goalie.
There is only one goalie in the hockey team.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 1

ii. Let B be the event that the captain selected will be a defender.
There are 6 defenders in the hockey team.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 2

Question 4.
Joseph kept 26 cards in a cap, bearing one English alphabet on each card. One card is drawn at random. What is the probability that the card drawn is a vowel card ?
Solution:
Each card bears an English alphabet.
∴ n(S) = 26
Let A be the event that the card drawn is a vowel card.
There are 5 vowels in English alphabets.
∴ A = {a, e, i, o, u}
∴ n(A) = 5
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 3
∴ The probability that the card drawn is a vowel card is \(\frac { 5 }{ 26 } \).

Question 5.
A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,
i. a red balloon.
ii. a blue balloon,
iii. a green balloon.
Solution:
Let the 2 red balloon be R1, R2,
3 blue balloons be B1, B2, B3, and
4 green balloons be G1, G2, G3, G4.
∴ Sample space
S = {R1, R2, B1, B2, B3, G1, G2, G3, G4}
∴ n(S) = 9

i. Let A be the event that Pranali gets a red balloon.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 4
∴ The probability that Pranali gets a red balloon is \(\frac { 2 }{ 9 } \)

ii. Let B be the event that Pranali gets a blue balloon.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 5
∴ The probability that Pranali gets a blue balloon is \(\frac { 1 }{ 3 } \).

iii. Let C be the event that Pranali gets a green balloon.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 6
∴ The probability that Pranali gets a green balloon is \(\frac { 4 }{ 9 } \).

Question 6.
A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?
Solution:
Let 5 red pens be R1, R2, R3, R4, R5.
8 blue pens be B1, B2, B3, B4, B5, B6, B7, B8. and
3 green pens be G1, G2, G3.
∴ Sample space
S = {R1, R2, R3, R4, R5, B1, B2, B3, B4, B5, B6, B7, B8, G1, G2, G3}
∴ n(S) = 16
Let A be the event that Rutuja picks a blue pen.
∴ A = {B1, B2, B3, B4, B5, B6, B7, B8}
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 7
∴ The probability that Rutuja picks a blue pen is \(\frac { 1 }{ 2 } \).

Question 7.
Six faces of a die are as shown below.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 8
If the die is rolled once, find the probability of
i. ‘A’ appears on upper face.
ii. ‘D’ appears on upper face.
Solution:
Sample space
S = {A, B, C, D, E, A}
∴ n (S) = 6
i. Let R be the event that ‘A’ appears on the upper face.
∴ R = {A, A}
∴ n(R) = 2
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 9

ii. Let Q be the event that ‘D’ appears on the upper face.
Total number of faces having ‘D’ on it = 1
Q = {D}
∴ n(Q) = 1
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 10
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 11

Question 8.
A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears
i. an odd number.
ii. a complete square number.
Solution:
Sample space,
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
∴ n(S) = 30

i. Let A be the event that the ticket drawn bears an odd number.
∴ A = {1,3,5,7,9,11,13,15,17,19,21, 23,25,27,29}
∴ n(A) =15
E:\Prasanna\Learncram\Class 10 Maths\ch 5\Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 14.png

ii. Let B be the event that the ticket drawn bears a complete square number.
∴ B = {1,4,9,16,25}
∴ n(B) = 5
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 13

Question 9.
Length and breadth of a rectangular garden are 77 m and 50 m. There is a circular lake in the garden having diameter 14 m. Due to wind, a towel from a terrace on a nearby building fell into the garden. Then find the probability of the event that it fell in the lake.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 14
Solution:
Area of the rectangular garden
= length × breadth
= 77 × 50
∴ Area of the rectangular garden = 3850 sq.m
Radius of the lake = \(\frac { 14 }{ 2 } \) = 7 m
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 15
∴ The probability of the event that the towel tell in the lake is \(\frac { 1 }{ 25 } \).

Question 10.
In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at
i. 8.
ii. an odd number.
iii. a number greater than 2.
iv. a number less than 9.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 16
Solution:
Sample space (S) = {1,2, 3, 4, 5, 6, 7, 8}
∴ n(S) = 8
i. Let A be the event that the spinning arrow comes to rest at 8.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 17
ii. Let B be the event that the spinning arrow comes to rest at an odd number.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 18
iii. Let C be the event that the spinning arrow comes to rest at a number greater than 2.
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 19
iv. Let D be the event that the spinning arrow comes to rest at a number less than 9.
∴ D = {1,2, 3, 4, 5, 6, 7, 8}
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 20

Question 11.
There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that a card drawn shows,
i. a natural number.
ii. a number less than 1.
iii. a whole number.
iv. a number greater than 5.
Solution:
Sample space (S) = {0, 1, 2, 3, 4, 5}
∴ n(S) = 6

i. Let A be the event that the card drawn shows a natural number.
∴ A = {1,2,3,4,5}
∴ n(A) = 5
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 21

ii. Let B be the event that the card drawn shows a number less than 1.
∴ B = {0}
∴ n(B) = 1
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 22

iii. Let C be the event that the card drawn shows a whole number.
∴ C = {0,1, 2, 3, 4, 5}
∴ n(C) = 6
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 23

iv. Let D be the event that the card drawn shows a number greater than 5.
Here, the greatest number is 5.
∴ Event D is an impossible event.
∴ D = { }
∴ n(D) = 0
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 24

Question 12.
A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is:
i. red.
ii. not red.
iii. either red or white.
Solution:
Let the three red balls be R1, R2, R3, three white balls be W1, W2, W3 and three green balls be G1, G2, G3.
∴ Sample space,
S = {R1, R2, R3, W1, W2, W3, G1, G2, G3}
∴ n(S) = 9

i. Let A be the event that the ball drawn is red.
∴ A = {R1, R2, R3}
∴ n(A) = 3
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 25

ii. Let B be the event that the ball drawn is not red.
B = {W1,W2,W3,G1,G2,G3}
∴ n(B) = 6
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 26

iii. Let C be the event that the ball drawn is red or white.
∴ C = {R1, R2, R3, W1, W2, W3}
∴ n(C) = 6
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 27

Question 13.
Each card bears one letter from the word ‘mathematics’. The cards are placed on a table upside down. Find the probability that a card drawn bears the letter ‘m’.
Solution:
Sample space
= {m, a, t, h, e, m, a, t, i, c, s}
∴ n(S) = 11
Let A be the event that the card drawn bears the letter ‘m’
∴ A = {m, m}
∴ n(A) = 2
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 28
∴ The probability that a card drawn bears letter ‘m’ is \(\frac { 2 }{ 11 } \).

Question 14.
Out of 200 students from a school, 135 like Kabaddi and the remaining students do not like the game. If one student is selected at random from all the students, find the probability that the student selected dosen’t like Kabaddi.
Solution:
Total number of students in the school = 200
∴ n(S) = 200
Number of students who like Kabaddi = 135
∴ Number of students who do not like Kabaddi
= 200 – 135 = 65
Let A be the event that the student selected does not like Kabaddi.
∴ n(A) = 65
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 29
∴ The probability that the student selected doesn’t like kabaddi is \(\frac { 13 }{ 40 } \).

Question 15.
A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a:
i. prime number.
ii. multiple of 4.
iii multiple of 11.
Solution:
Sample space
(S) = {10, 11, 12, 13, 14,
20, 21, 22, 23, 24,
30, 31, 32, 33, 34,
40, 41, 42, 43, 44}
∴ n(S) = 20

i. Let A be the event that the number so formed is a prime number.
∴ A = {11,13,23,31,41,43}
∴ n(A) = 6
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 30

ii. Let B be the event that the number so formed is a multiple of 4.
∴ B = {12,20,24,32,40,44}
∴ n(B) = 6
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 31

iii. Let C be the event that the number so formed is a multiple of 11.
∴ C = {11,22,33,44}
∴ n(C) = 4
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 32

Question 16.
The faces of a die bear numbers 0,1, 2, 3,4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.
Solution:
Sample space,
S = {(0, 0), (0,1), (0,2),
(1,0), (1,1), (1,2),
(2,0), (2,1), (2,2),
(3.0), (3,1), (3,2),
(4.0), (4,1), (4,2),
(5.0), (5,1), (5,2),
∴ n(S) = 36
Let A be the event that the product of digits on the upper face is zero.
∴ A = {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1,0), (2, 0), (3,0), (4, 0), (5,0)}
∴ n(A) = 11
Maharashtra Board Class 10 Maths Solutions Chapter 5 Probability Problem Set 5 33
∴ The probability that the product of the digits on the upper face is zero is \(\frac { 11 }{ 36 } \).

Class 10 Maths Digest

Practice Set 6.1 Algebra 10th Standard Maths Part 1 Chapter 6 Statistics Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 10 Maths Solutions covers the Practice Set 6.1 Algebra 10th Class Maths Part 1 Answers Solutions Chapter 6 Statistics.

10th Standard Maths 1 Practice Set 6.1 Chapter 6 Statistics Textbook Answers Maharashtra Board

Class 10 Maths Part 1 Practice Set 6.1 Chapter 6 Statistics Questions With Answers Maharashtra Board

Question 1.
The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 1
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 2
∴ The mean of the time spent by the students for their studies is 4.36 hours.

Question 2.
In the following table, the toll paid by drivers and the number of vehicles is shown. Find the mean of the toll by ‘assumed mean’ method.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 3
Solution:
Let us take the assumed mean (A) = 550
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 4
∴ The mean of the toll paid by the drivers is ₹ 521.43.

Question 3.
A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 5
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 6
∴ The mean of the milk sold is 2.82 litres.

Question 4.
A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by ‘assumed mean’ method.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 7
Solution:
Let us take the assumed mean (A) = 37.5
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 8
∴ The mean of the production of oranges is ₹ 35310.

Question 5.
A frequency distribution of funds collected by 120 workers in a company for the drought affected people are given in the following table. Find the mean of he funds by ‘step deviation’ method.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 9
Solution:
Here, we take A = 1250 and g = 500
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 10
∴ The mean of the funds collected is ₹ 987.5.

Question 6.
The following table gives the information of frequency distribution of weekly wages of 150 workers of a company. Find the mean of the weekly wages by ‘step deviation’ method.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 11
Solution:
Here, we take A = 2500 and g = 1000.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 12
∴ The mean of the weekly wages is ₹ 3070.

Question 1.
The daily sale of 100 vegetable vendors is given in the following table. Find the mean of the sale by direct method. (Textbook pg. no. 133 and 134)
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 13
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 14
The mean of the sale is 2150.

Question 2.
The amount invested in health insurance by 100 families is given in the following frequency table. Find the mean of investments using direct method and assumed mean method. Check whether the mean found by the two methods is the same as calculated by step deviation method (Ans: ₹ 2140). (Textbook pg. no. 135 and 136)
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 15
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 16
∴ The mean of investments in health insurance is ₹ 2140.
Assumed mean method:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 17
∴ The mean of investments in health insurance is ₹ 2140.
∴ Mean found by direct method and assumed mean method is the same as calculated by step deviation method.

Question 3.
The following table shows the funds collected by 50 students for flood affected people. Find the mean of the funds.
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 18
If the number of scores in two consecutive classes is very low, it is convenient to club them. So, in the above example, we club the classes 0 – 500, 500 – 1000 and 2000 – 2500, 2500 – 3000. Now the new table is as follows
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 19
i. Solve by direct method.
ii. Verily that the mean calculated by assumed mean method is the same.
iii. Find the mean in the above example by taking A = 1750. (Textbook pg. no. 137)
Solution:
i. Direct method:
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 20
∴ The mean of the funds is ₹ 1390.

ii. Assumed mean method:
Here, A = 1250
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 21
∴ The mean calculated by assumed mean method is the same.

iii. Step deviation method:
Here, we take A = 1750 and g = 250
Maharashtra Board Class 10 Maths Solutions Chapter 6 Statistics Practice Set 6.1 22
∴ The mean of the funds is ₹ 1390.

Class 10 Maths Digest

Practice Set 5.4 Algebra 10th Standard Maths Part 1 Chapter 5 Probability Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 10 Maths Solutions covers the Practice Set 5.4 Algebra 10th Class Maths Part 1 Answers Solutions Chapter 5 Probability.

10th Standard Maths 1 Practice Set 5.4 Chapter 5 Probability Textbook Answers Maharashtra Board

Class 10 Maths Part 1 Practice Set 5.4 Chapter 5 Probability Questions With Answers Maharashtra Board

Question 1.
If two coins are tossed, find the probability of the following events.
i. Getting at least one head.
ii. Getting no head.
Solution:
Sample space,
S = {HH, HT, TH, TT}
∴ n(S) = 4

i. Let A be the event of getting at least one head.
∴ A = {HT, TH, HH}
∴ n(A) = 3
∴ P(A) = \(\frac { n(A) }{ n(S) } \)
∴ P(A) = \(\frac { 3 }{ 4 } \)

ii. Let B be the event of getting no head.
∴ B = {TT}
∴ n(B) = 1
∴ P(B) = \(\frac { n(B) }{ n(S) } \)
∴ P(B) = \(\frac { 1 }{ 4 } \)
∴ P(A) = \(\frac { 3 }{ 4 } \); P(B) = \(\frac { 1 }{ 4 } \)

Question 2.
If two dice are rolled simultaneously, find the probability of the following events.
i. The sum of the digits on the upper faces is at least 10.
ii. The sum of the digits on the upper faces is 33.
iii. The digit on the first die is greater than the digit on second die.
Solution:
Sample space,
s = {(1,1), (1,2), (1,3), (1,4), (1, 5), (1,6),
(2, 1), (2, 2), (2,3), (2,4), (2, 5), (2,6),
(3, 1), (3, 2), (3, 3), (3,4), (3, 5), (3, 6),
(4, 1), (4, 2), (4,3), (4,4), (4, 5), (4,6),
(5, 1), (5, 2), (5,3), (5,4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6,4), (6, 5), (6,6)}
∴ n(S) = 36

i. Let A be the event that the sum of the digits on the upper faces is at least 10.
∴ A = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
∴ n(A) = 6
∴ P(A) = \(\frac { n(A) }{ n(S) } \) = \(\frac { 6 }{ 36 } \)
∴ P(A) = \(\frac { 1 }{ 6 } \)

ii. Let B be the event that the sum of the digits on the upper faces is 33.
The sum of the digits on the upper faces can be maximum 12.
∴ Event B is an impossible event.
∴ B = { }
∴ n(B) = 0
∴ P(B) = \(\frac { n(B) }{ n(S) } \) = \(\frac { 0 }{ 36 } \)
∴ P(B) = 0

iii. Let C be the event that the digit on the first die is greater than the digit on the second die.
C = {(2, 1), (3, 1), (3,2), (4,1), (4,2), (4, 3), (5, 1), (5,2), (5,3), (5,4), (6,1), (6,2), (6, 3), (6, 4), (6, 5),
∴ n(C) = 15
∴ P(C) = \(\frac { n(c) }{ n(S) } \) = \(\frac { 15 }{ 36 } \)
∴ P(C) = \(\frac { 5 }{ 12 } \)
∴ P(A) = \(\frac { 1 }{ 6 } \) ; P(B) = 0; P(C) = \(\frac { 5 }{ 12 } \)

Question 3.
There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn:
i. shows an even number.
ii. shows a number which is a multiple of 5.
Solution:
Sample space,
S = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15}
∴ n(S) = 15

i. Let A be the event that the ticket drawn shows an even number.
∴ A = {2, 4, 6, 8, 10, 12, 14}
∴ n(A) = 7
∴ P(A) = \(\frac { n(A) }{ n(S) } \)
∴ P(A) = \(\frac { 7 }{ 15 } \)

ii. Let B be the event that the ticket drawn shows a number which is a multiple of 5.
∴ B = {5, 10, 15}
∴ n(B) = 3
∴ P(B) = \(\frac { n(B) }{ n(S) } \) = \(\frac { 3 }{ 15 } \)
∴ P(B) = \(\frac { 1 }{ 5 } \)
∴ P(A) = \(\frac { 7 }{ 15 } \) ; P(B) = \(\frac { 1 }{ 5 } \)

Question 4.
A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is
i. an odd number?
ii. a multiple of 5?
Solution:
Sample space
(S) = {23, 25, 27, 29,
32, 35, 37, 39,
52, 53, 57, 59,
72, 73, 75, 79,
92, 93, 95, 97}
∴ n(S) = 20
i. Let A be the event that the number formed is an odd number.
∴ A = {23, 25, 27, 29, 35, 37, 39, 53, 57, 59, 73, 75,79,93,95,97}
∴ n(A) = 16
∴ P(A) = \(\frac { n(A) }{ n(S) } \) = \(\frac { 16 }{ 20 } \)
∴ P(A) = \(\frac { 4 }{ 5 } \)

ii. Let B be the event that the number formed is a multiple of 5.
∴ B = {25,35,75,95}
∴ n(B) = 4
∴ P(B) = \(\frac { n(B) }{ n(S) } \) = \(\frac { 4 }{ 20 } \)
∴ P(B) = \(\frac { 1 }{ 5 } \)
∴ P(A) = \(\frac { 4 }{ 5 } \) ; P(B) = \(\frac { 1 }{ 5 } \)

Question 5.
A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is
i. an ace.
ii. a spade.
Solution:
There are 52 playing cards.
∴ n(S) = 52
i. Let A be the event that the card drawn is an ace.
∴ n(A) = 4
∴ P(A) = \(\frac { n(A) }{ n(S) } \) = \(\frac { 4 }{ 52 } \)
∴ P(A) = \(\frac { 1 }{ 13 } \)

ii. Let B be the event that the card drawn is a spade.
∴ n(B) = 13
∴ P(B) = \(\frac { n(B) }{ n(S) } \) = \(\frac { 13 }{ 52 } \)
∴ P(B) = \(\frac { 1 }{ 4 } \)
∴ P(A) = \(\frac { 1 }{ 13 } \) ; P(B) = \(\frac { 1 }{ 4 } \)

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