Answer:
a The probability that at least one of the stocks will rise is 0.75
b The two given events can be seen to be not mutually exclusive
c The two given events can be seen to be not independent
Step-by-step explanation:
The probability that stock A will rise in price is, p(A) = 0.59
The probability that stock B will rise in price is, p(B) = 0.41
Given that stock B price goes up the stock A price will also go up is,
p(A | B) = 0.61.
a.) Now we know that
p(A | B) = [tex]\frac{p(A \cap B)}{p(B)}[/tex] = 0.61 .
Therefore [tex]p(A \cap B)[/tex] = p(B) ×0.61 = 0.41 × 0.61 = 0.25
the probability that at least one of the stocks will rise
= p( A ∪ B)
= p(A) + P(B) - [tex]p(A \cap B)[/tex]
= 0.59 + 041 - 0.25
= 0.75
b.) For mutually exclusive events we know that p(A | B) = 0 and this is not true in this case as p(A | B) = 0.61
The two events cannot be said to be mutually exclusive
c.) [tex]p(A \cap B) = p(A) \times p(B)[/tex] for independent events
If the two events have independence then
p(A|B) = [tex]\frac{p(A) \times p(B)}{p(B)} = p(A) \neq 0.61[/tex]
Therefore the events A and B are not independent.
