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Answer to Question #1872 in Statistics and Probability for Jenny
Question #1872
A problem in mathematics is given to three students A, B and C whose chances of solving it are 1/2, 3/4 and 1/4 respectively. What is the probability that the problem will be solved if all of them try independently.
Expert's answer
The probability that the problem is not solved by any of them:
(1 - P(A))*(1 - P(B))* (1 - P(C)) = (1 - 1/2)(1 - 3/4)(1 - 1/4) = 1/2*1/4*3/4 = 3/32
Hence, the probability that the problem will be solved is
1 - 3/32 = 29/32.
(1 - P(A))*(1 - P(B))* (1 - P(C)) = (1 - 1/2)(1 - 3/4)(1 - 1/4) = 1/2*1/4*3/4 = 3/32
Hence, the probability that the problem will be solved is
1 - 3/32 = 29/32.
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The probability that exactly one of them will solve it equals the following sum P(A)(1-P(B))(1-P(C))+(1-P(A))P(B)(1-P(C))+(1-P(A))(1-P(B))P(C)=1/2*1/4*3/4+1/2*3/4*3/4+1/2*1/4*1/4=3/32+9/32+1/32=13/32.
what is the probability that exactly one of them will solve it?
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Very helpful
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Thanks a lot ur suggestion helped me solve my problem
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