SOLUTION: Two girls, Anna and Cathy, attempt independently to solve a problem. The probability of Anna solving it is 0.60 and the probability of Cathy solving it is 0.30. Find the probabilit

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Question 395679: Two girls, Anna and Cathy, attempt independently to solve a problem. The probability of Anna solving it is 0.60 and the probability of Cathy solving it is 0.30. Find the probability that only one of them will be able to solve it.
Answer by jrfrunner(365) (Show Source):
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let p(A)=prob Anna solves the problem
let p(C)=prob Cathy solves the problem
let p(nA)=prob Anna does not solve the problem
let p(nC)=prob Cathy does not solve the problem
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Given P(A)=0.6, P(C)=0.3 and P(A), P(C) are independent
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P(nA)=1-P(A)=0.4 and P(nC)=0.7
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Find the probability that only one of them will be able to solve it.
=P(A and nC)+P(nA + C)
=P(A)P(nC)+P(nA)P(C) by independence
=0.6*0.7+0.4*0.3=0.42+0.12=0.54