Determine whether the events A and B are independent.

Question

P(A^c) = 0.2, P(B^c) = 0.4, P(A ∩ B) = 0.48

Answer 1

A and B are independent if P(A ∩ B) = P(A)P(B).

 

(Another way to say this is that when A and B are independent, P(A | B) = P(A) and P(B | A) = P(B) ).

 

Here,

P(A) = 1 - 0.2 = 0.8, and

P(B) = 1 - 0.4 = 0.6, so

P(A)P(B) = 0.8*0.6 = 0.48 = P(A ∩ B).

 

Therefore, the events A and B are independent, by the definition of independence given at the start.