Question

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

A.) 14/15
B.) 13/15
C.) 8/15
D.) 11/15

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)=(2)/(3)+(4)/(5)-(3)/(5)=(10+12-9)/(15) =(13)/(15)`

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