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प्रश्न
The probability that a person will get an electrification contract is `3/5` and the probability that he will not get plumbing contract is `5/8`. The probability of getting atleast one contract is `5/7`. What is the probability that he will get both?
उत्तर
Let A and B represent the event of getting electrification control and plumbing contract.
P(A) = `3/5`
`"P"(bar"B") = 5/8`
1 − P(B) = `5/8`
∴ P(B) = `1 - 5/8 = (8 - 5)/8`
P(B) = `3/8`
P(A ∪ B) = `5/7`
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
`5/7 = 3/5 + 3/8 - "P"("A" ∩ "B")`
P(A ∩ B) = `3/5 + 3/8 - 5/7`
= `(168 + 105 - 200)/280`
= `(273 - 200)/280`
= `73/280`
Probability of getting both the job is `73/280`
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