Symbiosis National Aptitude Test SNAP 2012 Paper

Question : 27 of 150

Marks: +1, -0

The probability that a contractor will get a plumbing contract 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?

31/45
8/45
14/45
None of these

Validate

Solution:

Let A be the event denotes that contractor gets the plumbing contract.
Let B be the event denotes that contractor gets the electric contract.
Given : P(A) =

2/3

, P(B) =

4/9

P(B↖{-})

5/9

and P (A ∪ B) =

4/5

To find : P (A ∩ B) = ?
We know, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒

4/5

2/3+4/9

- P (A ∩ B)
⇒ P (A ∩ B) =

{10}/9-4/5

{14}/{45}

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