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 0.80.

a. What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.)

b. Are events A and B mutually exclusive?

• Yes because P(A | B) = P(A).

• Yes because P(A ∩ B) = 0.

• No because P(A | B) ≠ P(A).

• No because P(A ∩ B) ≠ 0.

c. Are events A and B independent?

• Yes because P(A | B) = P(A).

• Yes because P(A ∩ B) = 0.

• No because P(A | B) ≠ P(A).

• No because P(A ∩ B) ≠ 0.

Answer 1

Solution:

A)

Let A be the event that Stock A will rise in price.

Let B be the event that Stock B will rise in price.

Therefore from the given probabilities:

P(A)=0.4 P(B)=0.6 P(A|B)=0.8 The probability that at least one of the stocks will rise in price calculated as: P(AB)- P(ANB) P(A\B)- P(B) P(ANB)=P(A|B)P(B) =0.8x0.6 = 0.48 Now, B ) P(AUB)=P(A)+P(B)-P(A =0.4+0.6-0.48 = 0.52

Therefore, the probability that at least one will rise = $P(A\cup B)$ = 0.52

B)

A and B are not mutually exclusive because.

PAB) +0

C)

A and B are not independent because of P(A | B) $\neq$ P(A).