Let A and B be events with probabilities PA 34 and PB 13 S

Let A and B be events with probabilities P(A) = 3/4 and P(B) = 1/3. Show that 1/12 P (A B) 1/3 and show that both upper and lower bounds are possible. Find corresponding bounds for P (A B).

Solution

as you can see if we multiply P(A)*P(B) = 3/4 * 1/3 = 1/4

so as you can see P(A intercept B) = P(A)*P(B) when they are independent so this probability is between the bounds