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The probability that a person will get an electric contract is 2/5 and the contract that he will not get plumbing contract is 4/7.If the probability of getting at least one contract is 2/3,what is the probability that he will get both?
A) 17/105 B) 17/106 C) 15/106 D) 18/106
Consider the following events: A=person gets an electric contract=person gets plumbing contract
We have,
P(A)=2/5,P(B)=4/7 and P(AUB)=2/3
Now (AUB)=P(A)+P(B)-P(A∩B)
=>2/3=2/5+(1-4/7)-P(A∩B)
=>P(A∩B)=2/3+3/7-2/3=17/105
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