Question

Given that events A and B are independent with P(A)=0.36 P(A)=0.36 and P(B∣A)=0.5 P(B∣A)=0.5, determine the value of P(B), rounding to the nearest thousandth, if necessary.

Answer 1

If events A and B are independent, then P(B|A) = P(B). We are given that P(A) = 0.36 and P(B|A) = 0.5, so we can use the formula for conditional probability to find P(A and B):

P(A and B) = P(B|A) * P(A)

P(A and B) = 0.5 * 0.36

P(A and B) = 0.18

Since A and B are independent, we also know that:

P(A and B) = P(A) * P(B)

Substituting the values we know, we get:

0.18 = 0.36 * P(B)

Solving for P(B), we get:

P(B) = 0.18 / 0.36

P(B) = 0.5

Therefore, the value of P(B) is 0.5.