If P(A) = 0.6, P(B)= 0.5, and P(A *B) =0.20, then P(B | A) =
A) .33.
B) .4.
C) .9.
D) .5.

Question

Quizplus · Accepted Answer

We can use the formula for conditional probability:

P(B | A) = P(A ∩ B) / P(A)

We know P(A ∩ B) = 0.20, and P(A) = 0.6. We still need to find P(B).

To do that, we can use the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We know P(A ∪ B) = 0.5 (since it's given that P(B) = 0.5), and we know the other two probabilities, so we can solve for P(B):

0.5 = 0.6 + P(B) - 0.20

0.5 = 0.4 + P(B)

P(B) = 0.1

Now we can plug in all the values to find P(B | A):

P(B | A) = P(A ∩ B) / P(A) = 0.20 / 0.6 = 0.33

So the answer is (B) .4.