If P(A) = 0.3, P(A
B) = 0.7, and P(A
B) = 0.2, then P(
B) = 0.2.

Question

If P(A) = 0.3, P(A 
B) = 0.7, and P(A 
B) = 0.2, then P(
B) = 0.2.

Quizplus · Accepted Answer

We can use Bayes' theorem to find P(B):
P(B) = P(B | A)*P(A) + P(B | not A)*P(not A)
We are given P(A) = 0.3, so P(not A) = 0.7. We are also given P(A and B) = 0.7, so:
P(B | A) = P(A and B)/P(A) = 0.7/0.3 = 2.33...
Similarly, P(B | not A) = P(not A and B)/P(not A) = P(B and not A)/0.7 = 0.2/0.7 = 0.2857...
Plugging these values into the equation above, we get:
P(B) = 2.33...*0.3 + 0.2857...*0.7
P(B) = 0.6999...
So the closest option is B, which is false - P(B) is not exactly equal to 0.2.