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Question
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5
State true or false: (give reason for your answer)
A' , B' ,C are mutually exclusive and exhaustive.
Options
True
False
Solution
This statement is False.
Since A' = B and B' = A,
A' ∩ B' = Φ
B ∩ C = {(1, 1), (1, 2), (1, 3), (1, 4), (3, 1), (3, 2)} ≠ Φ
A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} ≠ Φ
Thus, A', B' and C are not mutually exclusive.
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