(1) 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.
Solution:
Given Event A: Even number on the upper face.
Event B: Odd number on the upper face.
Event C: Prime number on the upper face.
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
(2) 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.
Solution:
Given 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.
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
(3) 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.
Solution:
Given 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
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