Question

The probabilities that stock A will rise in price is 0.52 and that stock B will rise in price is 0.48. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.68.

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

Probability:_______

b. Are events A and B mutually exclusive?

A. Yes because P(A | B) = P(A).

B. Yes because P(A ∩ B) = 0.

C. No because P(A | B) ≠ P(A).

D. No because P(A ∩ B) ≠ 0.

c. Are events A and B independent?

A. Yes because P(A | B) = P(A).

B. Yes because P(A ∩ B) = 0.

C. No because P(A | B) ≠ P(A).

D. No because P(A ∩ B) ≠ 0.

Answer 1

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

P(A&B) = P(A|B)*P(B) = 0.68 * 0.52 = 0.35

and P(A or B) = P(A) + P(B) - P(A&B)

= 0.52+0.48-0.35

=0.65

Probability: 0.65

b. Are events A and B mutually exclusive?

D. No because P(A ∩ B) ≠ 0

since P(A|B) = P(A&B)/P(B) = 0.68, obviously the numerator is non-zero which means that the 2 events are NOT mutually exclusive

c. Are events A and B independent?

C. No because P(A | B) ≠ P(A).

since P(A|B) is 0.68, while P(A) is 0.52, the 2 events are obviously NOT independent