Question

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?

Answer 1

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`