Question 189785: I am having trouble trying to set this problem up- could someone help please
thanks
Tom and Alice work independently in an attempt to solve a certain problem, i.e. whether one of them solves it does not affect the chances that the other will solve it. The probability that Tom solves it is 0.2 and the probability that Alice solves it is 0.4.
What is the probability that the problem will be solved?
If the problem is solved, what is the probability that Tom solves it?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Tom and Alice work independently in an attempt to solve a certain problem, i.e. whether one of them solves it does not affect the chances that the other will solve it. The probability that Tom solves it is 0.2 and the probability that Alice solves it is 0.4.
What is the probability that the problem will be solved?
P(solved) = P(solved and Tom) + P(solved and Alice)
= P(solved|Tom)*P(Tom) = P(solved|Alice)*P(Alice)
= 0.2*(1/2) + 0.4*(1/2) = (1/2)(0.6) = 0.3
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If the problem is solved, what is the probability that Tom solves it?
P(Tom|solved) = P(Tom and solved)/P(solved)
= [(1/2)(0.2)]/0.3 = 0.1/0.3 = 1/3
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Cheers,
Stan H.
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