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.
