Question

The probabilities that stock A will rise in price is 0.59 and that stock B will rise in price is 0.41. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.61. a. What is the probability that at least one of the stocks will rise in price.b. Are events A and B mutually exclusive? i. Yes because P(A | B) = P(A).ii. Yes because P(A ∩ B) = 0.iii. No because P(A | B) ≠ P(A).iv. No because P(A ∩ B) ≠ 0.c. Are events A and B independent? i. Yes because P(A | B) = P(A).ii.Yes because P(A ∩ B) = 0.iii.No because P(A | B) ≠ P(A).iv.No because P(A ∩ B) ≠ 0.

Answer 1

Answer:

1) 0.75

2) No, the 2 events are not mutually exclusive because P(A&B) ≠ 0

3)The 2 events are not independent because P(A | B) ≠ P(A).

Step-by-step explanation:

1) P(A) = 0.59 and P(B) = 0.41

Thus; to find the probability that at least one of the stocks will rise in price;

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

Now, we know that if B rises in price, the probability that A will also rise is 0.61 i.e P(A|B) = 0.61

Hence;P(A & B) = P(A|B) x P(B) =0.61 x 0. 41 = 0.25

So P(A or B) = 0.59 + 0.41 - 0.25 = 0.75

B) we want to find out if events A and B are mutually exclusive ;

P(A|B) = P(A&B)/P(B), For the events to be mutually exclusive, P(A&B) has to be zero. Since P(A&B) ≠ 0,the 2 events are not mutually exclusive.

C) Since P(A|B) = 0.61 and P(A) is 0.59. Thus, P(A | B) ≠ P(A).

So, therefore the 2 events are not independent.