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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 and C are mutually exclusive
Options
True
False
Solution
This statement is False.
Reason:
A = even number on the first dice
C = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1}}
A and C have (2, 1), (2, 2), (2, 3), (4, 1) as equal events.
∴ A ∩ C ≠ ϕ
Hence, A and C are not mutually exclusive.
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