Practice Set 5.3

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

###### Practice Set 5.3

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).

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