Answer:
P(B) = 0.85
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
[tex]P(A) = 0.24, P(B|A) = 0.85[/tex]
These events are independent.
This means that [tex]P(A \cap B) = P(A)*P(B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(B|A) = \frac{P(A)*P(B)}{P(A)}[/tex]
[tex]P(B|A) = P(B)[/tex]
So
[tex]P(B) = 0.85[/tex]
