Question

If P(A) = 0.25, P(B) = 0.60 and P(A and B) = 0.15, are the event A and B independent? Explain/show work.

Answer 1

event A and B are independent because P(A and B) = P(A) x P(B) = 0.15

Explanation:

When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;

P(A and B) = P(A) x P(B)

Given;

P(A) = 0.25

P(B) = 0.60

P(A and B) = 0.15

Now, let's check if P(A and B) will be equal to P(A) x P(B)

P(A) x P(B) = 0.25 x 0.60 = 0.15

P(A and B) = P(A) x P(B), thus event A and B are independent.