SOLUTION: Two computers A and B are to be marketed. A salesman who is assigned the job of finding customers for them has 70% and 30% chances respectively of succeeding in case of computer A
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Question 1166038: Two computers A and B are to be marketed. A salesman who is assigned the job of finding customers for them has 70% and 30% chances respectively of succeeding in case of computer A and B. The computers can be sold independently. Given that he was able to sell at least one computer, what is the probability that the computer A has been sold? Answer by ikleyn(52887) (Show Source):
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Two computers A and B are to be marketed. A salesman who is assigned the job of finding customers for them has 70% and 30%
chances respectively of succeeding in case of computer A and B. The computers can be sold independently.
Given that he was able to sell at least one computer, what is the probability that the computer A has been sold?
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The key to solving this problem is hidden in THIS phrase
The computers can be sold independently.
Actually, in the hidden form, this phrase represents the following statement:
The probability to sell both computers simultameously P(A and B) is the product P(A) and P(B):
P(A and B) = P(A)*P(B).
Having it deciphered, we are in one step from the solution.
1) The probability that at least one computer is sold is
P(A and B) = P(A) + P(B) - P(A and B) = P(A) + P(B) - P(A)*P(B) = 0.7 + 0.3 - 0.7*0.3 = 1 - 0.21 = 0.79.
2) The probability that the computer A has been sold given that at least one computer was sold is this CONDITIONAL probability
P(A sold | at least one of A or B was sold) = = = 0.886 = 88.6%. ANSWER
