Let PA 0 5 PB 08 PA B 04 a Are A and B mutually exclusive

Let P(A) =0 .5, P(B) = 0.8, P(A ? B) = 0.4,

(a) Are A and B mutually exclusive (disjoint)? Why?

(b) Are A and B independent? Why?

a) They are not disjoint because P(a n B) is not 0
So, they do have something in common, which is why they are not disjoint

b)
P(A) * P(B) = 0.5 * 0.8 = 0.4
As we can see this is also the value of P(A n B)
Sicne P(A) * P(B) = P(A n B), they are independent

c)
P(A u B) = P(A) + P(B) - P(A n B)
P(A u B) = 0.5 + 0.8 - 0.4
P(A u B) = 0.9