Suppose p(a) = 0.40 and p(a  b.= 0.55. find p(b) if … a.… p(a  b.= 0.30; b.… p(a  b.= 0.45; c.… a and b are mutually exclusive; d.… a and b are independent.

Between the probability of union and intersection, it's not clear what you're supposed to compute. (I would guess it's the probability of union.) But we do know that



For parts (a) and (b), you're given everything you need to determine .

For part (c), if and are mutually exclusive, then , so . If the given probability is , then you can find . But if this given probability is for the intersection, finding is impossible.

For part (d), if and are independent, then .