If P(A) = 0.80, P(B) = 0.65, and P(A $\cup$ B) = 0.78, then P(B|A) =
A)0.6700
B)0.8375
C)0.9750
D)Not enough information is given to answer this question.

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 that P(A) = 0.80, P(B) = 0.65, and P(A ∪ B) = 0.78.

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

P(A ∩ B) = 0.80 + 0.65 - 0.78

P(A ∩ B) = 0.67

Now we can plug in the values into Bayes' theorem:

P(B|A) = 0.67 / 0.80

P(B|A) = 0.8375

Therefore, the answer is B.

If P(A) = 0 ∪\cup∪ B) = 078, Then P(B|A) = A)0

If P(A) = 0 $\cup$ B) = 078, Then P(B|A) =
A)0