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Question
The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ______.
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Solution
The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is 0.2.
Explanation:
Given that: P(A) = 0.5, P(B) = 0.3
And P(A ∩ B) = 0 .....[∵ A and B are mutually exclusive events]
∴ `P(barA ∩ barB) = P(bar(A ∪ B))`
= 1 – P(A ∪ B)
= 1 – [P(A) + P(B)]
= 1 – (0.5 + 0.3)
= 1 – 0.8
= 0.2
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