Question

Exercise 4-27 Algo The probabilities that stock A will rise in price is 0.56 and that stock B will rise in price is 0.44. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.48. 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? Yes because PA | B) P(A) Yes because P(A n B) 0. No because P(A | B) P(A). No because P(A n B)0. c. Are events A and B independent? Yes because PA | B) P(A) Yes because PAn B)0 No because P(A B) P(A). O No because P(A n B) #0.

Answer 1

Given, P(A) = 0.56, P(B) = 0.44 and P(A | B) = 0.48,

$P(A | B) = \frac{P(A \cap B)}{P(B)}$

So, $P(A \cap B) = P(A | B) * P(B) = 0.48 * 0.44 = 0.2112$

(a)

Probability that at lease one stock price will rise,

$P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.56 + 0.44 - 0.2112 = 0.79$ (Ans)

(b)

No because, $P(A \cap B) = 0.2112 \neq 0$

(c)

No because, $P(A | B) \neq P(A)$

** If these answers do not match please comment.