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Question
The probability of the event A occurring is `1/3` and of the event B occurring is `1/2`. If A and B are independent events, then find the probability of neither A nor B occurring.
Solution
Given P(A) = `1/3` and P(B) = `1/2`
∵ A and B are independent events.
So `bar"A"` and `bar"B"` are also independent events.
∴ Required probability
`"P"(bar"A" ∩ bar"B") = "P"(bar"A")xx"P"(bar"B")`
= `(1 - 1/3)xx(1 - 1/2)`
= `2/3 xx 1/2`
= `1/3`
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