Question

Let two events A and B have the following properties: P(A) = 0.5, P(B) = 0.4, and P(B|A) = 0.6. Find P(A and B).

Answer 1

The probability of both events A and B occurring together, given P(A) = 0.5, P(B) = 0.4, and P(B|A) = 0.6, is calculated as 0.3 by multiplying P(B|A) with P(A).

Step-by-step explanation:

The question involves finding the probability of the intersection of two events, A and B. Given P(A) = 0.5, P(B) = 0.4, and P(B|A) = 0.6, the probability of both events occurring simultaneously, denoted as P(A and B), can be found using the formula P(A and B) = P(B|A) × P(A).

Plugging in the given values:

P(A and B) = P(B|A) × P(A)

P(A and B) = 0.6 × 0.5

P(A and B) = 0.3

So, the probability of both events A and B happening together is 0.3.