The probability that a computer company will get a computer hardware contract is 4/5 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 5/6, what is the probability that it will get both the contracts? Choose the most appropriate option: A) 7/20 B) 9/25 C) 11/30 D) 13/35 E) 17/40
Let, A ≡ event of getting hardware contract   B ≡ event of getting software contract   AB ≡ event of getting both hardware and software contract.   P(A) = 4/5, P(~B) =5/9   =&gt; P(B) = 1- (3/5) = 2/5.   A and B are not mutually exclusive events but independent events. So,   P(at least one of A and B ) = P(A) + P(B) - P(AB).   =&gt; 5/6 = (4/5) + (2/5) - P(AB).   =&gt; P(AB) = 11/30.   Hence, the required probability is 11/30.   The answer is 11/30.
<result>C</result>
The probability that a computer company will get a computer hardware contract is 4/5 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 5/6, what is the probability that it will get both the contracts?