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.

Answer 1

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`