Question on probability

Q. The probability that Nike will get Cricket team contract is 2/3 and the probability that Nike will get Hockey team contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability of getting both the contract? a. 19/45 b. 13/45 c. 12/35 d. 11/23

Anyone can help me in

Anyone can help me in solving the above question i got it from this site only and it is on QBM004

The probability that Nike

The probability that Nike will get Cricket team contract = P (A) = 2/3 The probability that Nike will get Hockey team contract = p (B) = 5/9 The probability of getting at least one contract = p (A U B)= 4/5 Tthe probability of getting both the contract = P (A ∩ B) Its a simple forumla

P(A U B) = P(A) + P(B) - P(A ∩ B)
and the answer is 19/45