SOLUTION: A company has created two teams to design a new product. The probability that team A is successful is 2/3. The probability that team B is successful is 1/2. The probability that

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Question 1163708: A company has created two teams to design a new product.
The probability that team A is successful is 2/3.
The probability that team B is successful is 1/2.
The probability that at least one team is successful is ¾.
Assume exactly one team was successful.
What is the probability that it was designed by Team B?
Answer by greenestamps(13203) About Me  (Show Source):
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P(A successful) = 2/3 = 8/12

P(B successful) = 1/2 = 6/12

P(A or B (or both) successful) = 3/4 = 9/12

P(A successful but not B) = 9/12 - 6/12 = 3/12

P(B successful but not A) = 9/12 - 8/12 = 1/12

P(only one team successful) = 3/12 + 1/12 = 4/12

P(B successful, given that only one team was successful) = (1/12)/(4/12) = 1/4

ANSWER: 1/4