From basic probability we know that if A and B are any two events in the sample space, S, then:
[tex] P(A\cup B)=P(A)+P(B)-P(A\cap B) [/tex]
[tex] \therefore P(A\cap B)=P(A)+P(B)-P(A\cup B) [/tex]......(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:
[tex] P(A\cap B)=\frac{2}{3}+\frac{4}{5}-\frac{3}{5}=\frac{10+12-9}{15} =\frac{13}{15} [/tex]
This matches Option B. Therefore, Option B is the correct answer.