Question

The probability that a contractor will get a plumbing contract is 0.4 and the probability that he will not get an electric contract is 0.7. If the probability of getting at least one contract is 0.6, what is the probability that he will get: both the contracts and exactly one contract.

Answer 1

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Answer 2

The probability that he will get both is 0.1.

Step-by-step explanation:

Since we have given that

Probability that a contractor will get a plumbing contract = 0.4

Probability that a contractor will not get an electric contract = 0.7

Probability that a contractor will get an electric contact = 1-0.7 =0.3

Probability that getting at least one contract =

So, we need to find the probability that he will get both the contracts and exactly one contract.

So, it becomes,

$P(P\cap E)=P(P)+P(E)-P(P\cup E)\\\\0.6=0.4+0.3-x\\\\0.6=0.7-x\\\\0.6-0.7=-x\\\\-0.1=-x\\\\x=0.1$

Hence, the probability that he will get both is 0.1.

# learn more:

The probability that a contractor will get a plumbing contract is 2/3, probability that he will not get an electrical 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?

https://brainly.in/question/3243203