Question

If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∪ B')

Answer 1

Here, P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2`

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
∴ P(A ∩ B) = P(A) + P(B) − P(A ∪ B)
= `1/4+2/5-1/2`

= `3/20`

P(A' ∪ B')  = P(A ∩ B)`  ...[De Morgan's law]
= 1 – P(A ∩ B)

= `1 - 3/20`

= `17/20`