Answer:
P(A and B) = 0.1 = 10%
Step-by-step explanation:
Conditional Probability
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, we have that:
[tex]P(A) = 0.2, P(B|A) = 0.5[/tex]
What is P(A and B)?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)*P(A) = 0.5*0.2 = 0.1[/tex]
P(A and B) = 0.1 = 10%
