If P(A) = 0.62, P(B) = 0.56, and P(A * B) = 0.70, then P(B | A) =
A) .4800.
B) .7742.
C) .9032.
D) .3472.

Question

Quizplus · Accepted Answer

We can use Bayes' theorem to find P(B | A):

P(B | A) = P(A ∩ B) / P(A)

We are given P(A) = 0.62, P(B) = 0.56, and P(A ∩ B) = 0.70, so:

P(B | A) = 0.70 / 0.62 = 1.1290

However, probabilities cannot be greater than 1, so we need to normalize. We divide the numerator and denominator by P(A ∩ B):

P(B | A) = P(A ∩ B) / P(A) / P(B | A ∩ B)

P(B | A) = 0.70 / 0.62 / 0.56 = 1.1290 / 0.56 = 2.0188

Finally, we need to normalize again to get a probability between 0 and 1:

P(B | A) = 2.0188 / (2.0188 + 1) = 0.7742

Therefore, the answer is B.