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# The Probability that a Contractor Will Get a Plumbing Contractor is 2 3 . and the Probability that He Will Not Get an Electric Contract is 5 9 . If the Probability of Getting at Least One Contrac - Mathematics

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MCQ

The probability that a contractor will get a plumbing contractor is 2/3. and the probability that he will not get an electric contract is 5/9. If the probability of getting at least one contract is 4/5 what is the probability that he will get both?

#### Options

• 16/45

• 13/45

• 14/45

• 15/72

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#### Solution

14/45

Explanation:

Let the probability of getting plumbing contract P(A) = 2/3

and the probability of getting an electric contract P(B) = 1 - P (not getting electric contract)

= 1-5/9=4/9

Also, P(A∪B) = 4/5

Required probability, P (A∩B)
= P(A) + P(B) - P(A∪B)

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

= (30+20-36)/45=14/45

Concept: Probability (Entrance Exam)
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