Practice Set 5.3 Probability Class 10th Mathematics Part 1 MHB Solution

Practice Set 5.3

1. One die is rolled, Event A : Even number on the upper face. Event B : Odd number on…
2. Two dice are rolled simultaneously, Event A : The sum of the digits on upper faces is…
3. Three coins are tossed simultaneously. Condition for event A : To get at least two…
4. Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the…
5. From three men and two women, environment committee of two persons is to be formed.…
6. One coin and one die are thrown simultaneously. Condition for event A : To get…

Practice Set 5.3

Question 1.

Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).

One die is rolled,

Event A : Even number on the upper face.

Event B : Odd number on the upper face.

Event C : Prime number on the upper face.

Answer:

Sample space, S = {1, 2, 3, 4, 5, 6}

Number of sample points, n(S) = 6

A = {2, 4, 6} , n(A) = 3

B = {1, 3, 5} , n(B) = 3

C = {2, 3, 5} , n(C) = 3

Question 2.

Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).

Two dice are rolled simultaneously,

Event A : The sum of the digits on upper faces is a multiple of 6.

Event B : The sum of the digits on the upper faces is minimum 10.

Event C : The same digit on both the upper faces.

Answer:

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)}

Number of sample points, n(S) = 36

A = {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (6, 6)}, n(A) = 6

B = {(4, 6) (5, 5) (5, 6) (6, 4) (6, 5) (6, 6)} , n(B) = 6

C = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)} , n(C) = 6

Question 3.

Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).

Three coins are tossed simultaneously.

Condition for event A : To get at least two heads.

Condition for event B : To get no head.

Condition for event C : To get head on the second coin.

Answer:

Sample Space, S = {HHH, HHT, HTT, HTH, THT, TTH, THH, TTT}

Number of sample points, n(S) = 8

To get at least two heads ,A = {HHH, HHT, HTH, THH}

n(A) = 4

To get no head, B = {TTT}

n(B) = 1

To get head on the second coin ,C = {HHH, HHT, THH}

n(C) = 3

Question 4.

Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).

Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits.

Condition for event A : The number formed is even

Condition for event B : The number formed is divisible by 3.

Condition for event C : The number formed is greater than 50.

Answer:

Sample Space, S= {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43,45, 50, 51, 52, 53, 54}

Number of sample points, n(S) = 25

The number formed is even , A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}

n(A) = 13

The number formed is divisible by 3, B = {12, 15, 21, 24, 30, 42, 45, 51, 54}

n(B) = 9

The number formed is greater than 50,C = {51, 52, 53, 54} n(C) = 4

Question 5.

Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).

From three men and two women, environment committee of two persons is to be formed.

Condition for event A : There must be at least one woman member.

Condition for event B : One man, one woman committee to be formed

Condition for event C : There should not be a woman member.

Answer:

Sample Space, S = {M1M2, M1M3, M1F1, M1F2, M2M3, M2F1, M2F2, M3F1, M3F2, F1F2}

Number of sample points, n(S) = 10

There must be at least one woman member , A = {M1F1, M1F2, M2F1, M2F2, M3F1, M3F2, F1F2}

n(A) = 7

One man, one woman committee to be formed , B = {M1F1, M1F2, M2F1, M2F2, M3F1, M3F2}

n(B) = 6

There should not be a woman member , C = {M1M2, M1M3, M2M3}

n(C) = 3

Question 6.

Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).

One coin and one die are thrown simultaneously.

Condition for event A : To get head and an odd number.

Condition for event B : To get a head or tail and an even number.

Condition for event C : Number on the upper face is greater than 7 and tail on the coin.

Answer:

Sample Space, S = {H1, H2, H3, H4, H5, H6 T1, T2, T3, T4, T5, T6}

Number of sample points, n(S) = 12

To get head and an odd number , A = {H1, H3, H5}

n(A) = 3

To get a head or tail and an even number , B = {H2, H4, H6, T2, T4, T6}

n(B) = 6

Number on the upper face is greater than 7 and tail on the coin= No Sample space exists for this event as dice does not have numbers greater than or equal to 7

n(C)=0