Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# The probability that a person will get an electrification contract is 35 and the probability that he will not get plumbing contract is 58. The probability of getting atleast one contract is 57. What - Mathematics

Sum

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?

#### Solution

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

Concept: Algebra of Events
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