Question

If P(A) = 3/4, P(B)=1/2, and P(AB)=7/8, what is P(AB)?
a. 5/8
b7/8
c3/8
d1/8

Answer 1

We know that P(AB) = P(A) + P(B) - P(A∪B), where P(A∪B) represents the probability that at least one of the events A or B will occur.

To calculate P(A∪B), we can use the formula P(A∪B) = P(A) + P(B) - P(AB), which follows from the addition rule of probability.

Substituting with the given values, we have:

P(A∪B) = P(A) + P(B) - P(AB)

P(A∪B) = 3/4 + 1/2 - 7/8

P(A∪B) = 6/8 + 4/8 - 7/8

P(A∪B) = 3/8

Now, we can calculate P(AB) using the first formula:

P(AB) = P(A) + P(B) - P(A∪B)

P(AB) = 3/4 + 1/2 - 3/8

P(AB) = 6/8 + 4/8 - 3/8

P(AB) = 7/8

Therefore, the correct answer is option b) 7/8.

Explanation: