The probabilities that Mensah will pass a mathematics and an economics test are 3/4 and 5/8 respectively. If the probability that he passes at least one of the subject is 7/12 what is the probability that he passes both subject?

Answer 1

Let A be the event that Mensah passes the mathematics test and B be the event that he passes the economics test.

We are given:
P(A) = 3/4
P(B) = 5/8
P(A U B) = 7/12

We want to find P(A ∩ B) - the probability that Mensah passes both subjects.

From the formula for the union of two events:
P(A U B) = P(A) + P(B) - P(A ∩ B)

Substitute in the known values:
7/12 = 3/4 + 5/8 - P(A ∩ B)
7/12 = 6/8 + 5/8 - P(A ∩ B)
7/12 = 11/8 - P(A ∩ B)
P(A ∩ B) = 11/8 - 7/12
P(A ∩ B) = 33/24 - 14/24
P(A ∩ B) = 19/24

Therefore, the probability that Mensah passes both subjects (mathematics and economics) is 19/24.