Question

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.

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

Let A be the event that stock A will rise in price and B be the event that stock B will rise in price.

Given that, P(A) = 0.46

P(B) = 0.54

P(A | B) = 0.16

According to Bayes' theorem, P(A | B) = P(A B) / P(B)

Therefore, 0.16 = P(A B) / 0.54

P(A B) = 0.09

a) P(at least one stock will rise in price), P(A U B) = P(A) + P(B) - P(A B)

= 0.46 + 0.54 - 0.09

= 0.91

b) If two events are mutually exclusive, P(A B) = 0

Here, P(A B) 0. therefore, A and B are not mutually exclusive.

Ans: No because P(A B) 0

c) If A and B are independent, P(A) = P(A | B)

Here, P(A) P(A |B) and hence, A and B are not independent.

Ans: No because P(A | B) P(A)

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