1.

The probability for a contractor to get a road contract is 2/3 and to get a building contract is 5/9. The probability to get at least one contract is 4/5. Find the probability that he gets both the contracts.

Answer»

Suppose A is the event of getting a road contract.

B is the event of getting a building contract

Given P(A) = 2/3; P(B) = 5/9; P(A ∪ B) = 4/5

P(A ∪ B) =P(A) + P(B) – P(A ∩ B)

P(A ∩ B) =P(A) + P(B) – P(A ∪ B)

= 2/3 + 5/9 - 4/5

= (30 + 25 - 36)/45 = 19/45

Probability to get both contracts = 19/45



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