Question

If P(A)=2/3, P(B)= 4/5 and P(A U B) = 3/5, what is P(A u B)?

Answer 1

From basic probability we know that if A and B are any two events in the sample space, S, then:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$\therefore P(A\cap B)=P(A)+P(B)-P(A\cup B)$......(Equation 1)

In the question we have been given all the data that is required. Thus, we have: P(A)=2/3, P(B)= 4/5 and P(A U B) = 3/5.

Substituting these values in (Equation 1) we get:

$P(A\cap B)=\frac{2}{3}+\frac{4}{5}-\frac{3}{5}=\frac{10+12-9}{15} =\frac{13}{15}$

This matches Option B. Therefore, Option B is the correct answer.