The probability that a contractor will get a plumbing contract is 23 and an electric contract is 49.If the probability of getting at least one contract is 45,find the probability that he will get both the contracts.
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P(Plumbing)=23
P(Electric)=49
P(PUE)=45 -------(Probability of getting both contracts)
we know,
P(PUE) = P(P) + P(E) - 2P(P∩E)
45 = 23 + 49 - 2P(P∩E)
45 = 72 - 2P(P∩E)
or 2P(P∩E) = 72-45
P(P∩E) = 27
P(P∩E) = 27/2
P(P∩E) = 13.5
hence, the probability of getting both the contracts is 13.5
P(Electric)=49
P(PUE)=45 -------(Probability of getting both contracts)
we know,
P(PUE) = P(P) + P(E) - 2P(P∩E)
45 = 23 + 49 - 2P(P∩E)
45 = 72 - 2P(P∩E)
or 2P(P∩E) = 72-45
P(P∩E) = 27
P(P∩E) = 27/2
P(P∩E) = 13.5
hence, the probability of getting both the contracts is 13.5
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