Question

If P(A)=2/3 P(B) = 4/5 and P(A u B)= 11/15 what is P(A n B)?

a. 8/15
b. 11/15
c. 13/15
d. 14/15

Answer 1

(b) 11/15

Explanation:

We can use the formula:

P(A U B) = P(A) + P(B) - P(A n B)

where P(A n B) is the probability of the intersection of events A and B.

We are given:

P(A) = 2/3

P(B) = 4/5

P(A U B) = 11/15

Substituting these values into the formula, we get:

11/15 = 2/3 + 4/5 - P(A n B)

To solve for P(A n B), we can simplify the right-hand side:

11/15 = 10/15 + 12/15 - P(A n B)

11/15 = 22/15 - P(A n B)

P(A n B) = 22/15 - 11/15

P(A n B) = 11/15

Therefore, the answer is (b) 11/15.