# If P(A) = 14, P(B) = 25 and P(A ∪ B) = 12 Find the value of the following probability: P(A' ∩ B') - Mathematics and Statistics

Sum

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')

#### Solution

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

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

= 1 - 1/2
= 1/2