The probability that a computer company will get a computer hardware contract is 2/3 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts ?  Choices.
A) 14/45 B) 4/9 C) 4/5 D) 4/6 E) None of these
Explanation :   Let, A ≡ event of getting hardware contract   B ≡ event of getting software contract   AB ≡ event of getting both hardware and software contract.   P(A) = 2/3, P(~B) =5/9   =&gt; P(B) = 1- (5/9) = 4/9.   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; 4/5 = (2/3) + (4/9) -P(AB).   =&gt; P(AB) = 14/45.   Hence, the required probability is 14/45.   14/45nswer : 14/45
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The probability that a computer company will get a computer hardware contract is 2/3 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts ?