Question

Let a and b be events with p(a) = 0.8, p(b) = 0.4, and p(b|a) = 0.2. Find p(a and b)?

Answer 1

The probability that both events A and B occur together, denoted as P(A and B), is calculated using the formula P(A and B) = P(B|A) × P(A). With P(B|A) = 0.2 and P(A) = 0.8, P(A and B) is 0.16.

Step-by-step explanation:

The student is asking to find the probability of both events A and B occurring together, which is denoted as P(A and B). According to the conditional probability formula:

P(A and B) = P(B|A) × P(A)

From the given information, we have:

P(B|A) = 0.2 (the probability of B given A)

P(A) = 0.8 (the probability of A)

Now we can calculate P(A and B):

P(A and B) = 0.2 × 0.8 = 0.16

Thus, the probability that both events A and B occur together is 0.16.