If 2P(A) = P(B) = 5/13 and P(AIB) = 2/5 then the value of P(AUB) is-

It is given that 2P(A) = P(B) = 5/13 and P(AIB) = 2/5

⇒  P(A) = 5/26  and P(B)=5/13 

and P(AIB) = 2/5

 We know that P(AIB) = P(A∩B)/ P(B)

⇒  2/5 = P(A∩B)/ P(B)

⇒  P(A∩B) = 2/5x P(B)

⇒  P(A∩B) = (2/5)x (5/13) = 2/13

We know that P(A∪B) = P(A) +P(B) -P(A∩B)

                  ⇒ P(A∪B) = (5/26) + (5/13) - (2/13)

                 ⇒ P(A∪B) = 11/26