The probability that the contractor will get a plumbing contract is 2/3 and an electric contract is 4/9 .If the probability of getting at least one contract is 4/5 .Find the probability that he will get both the projects
Let
Probability that the contractor will get a plumbing contract, P (A) = 2/3___________(1)
Probability that the contractor will get an electric contract, P (B) = 4/9_____________(2)
Probability of getting at least one contract is 4/5
Implies P(AUB)= 4/5
i.e., P(AUB)=P(A)+P(B)-P(AB)= 4/5_____________(3)
We have to find the probability that he will get both the projects,
i.e., P(AB)=?
So, from (3),
P(AB)=P(A)+P(B)-P(AUB)
Therefore,
P(AB) =2/3 + 4/9 – 4/5
=14/45
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