Question

The probabilities that stock A will rise in price is 0.40 and that stock B will rise in price is 0.60. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.50. a. What is the probability that at least one of the stocks will rise in price?

Answer 1

Answer:

The probability that at least one of the stocks will rise in price is 0.70.

Step-by-step explanation:

The conditional probability of event X given that another event Y has already occurred is:

$P(X|Y)=\frac{P(X\cap Y)}{P(Y)}$

Denote the events as follows:

A = stock A rises in price

B = stock B rises in price

Given:

P (A) = 0.40

P (B) = 0.50

P (A|B) = 0.50

Compute the value of P (A ∩ B) as follows:

$P(A|B)=\frac{P(A\cap B)}{P(B)}\\P(A\cap B)=P(A|B)P(B)\\=0.50\times0.60\\=0.30$

The probability that at least one of the stock rises is same as the probability of either stock A or B rising.

Compute the value of P (A ∪ B) as follows:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\=0.40+0.60-0.30\\=0.70$

Thus, the probability that at least one of the stocks will rise in price is 0.70.