Question

P(A) = 20%. P(B) = 50%. P(BIA) = P(B). What is P(A and B)?

Answer 1

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question, we have that:

$P(A) = 0.2, P(B|A) = 0.5$

What is P(A and B)?

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(A \cap B) = P(B|A)*P(A) = 0.5*0.2 = 0.1$

P(A and B) = 0.1 = 10%