If A and B are independent events show that A' and B are also independent.

Solution:

Given A and B are independent events.

So, P(A ∩ B) = P(A) P(B)

Now, P(A' ∩ B) = P(B) - P(A ∩ B)

= P(B) -P(A)P(B)

=P(B)[1-P(A)]

=P(B).P(A')

So, P(A' ∩ B) = P(B).P(A')

Hence proved.

If A and B are independent events show that A' and B are also independent.

Summary:

If A and B are independent events then A' and B are also independent.