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
