The probabilities that stock A will rise in price is 046 and

The probabilities that stock A will rise in price is 0.46 and that stock B will rise in price is 0.54. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.16.

What is the probability that at least one of the stocks will rise in price?

Solution

Let

A = A rises
B = B rises

Hence,

P(A) = 0.46

P(B) = 0.54

P(A|B) = 0.16

Hence

P(A n B) = P(A|B) P(B) = 0.16*0.54 = 0.0864

Thus,

P(A U B) = P(A) + P(B) - P(A n B)

= 0.46 + 0.54 - 0.0864

P(A U B) = 0.9136 [ANSWER]