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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Assignment Expert04.03.14, 17:54You're welcome. We are glad to be helpful. If you really liked our service please press like-button beside answer field. Thank you!

JeeJa04.03.14, 09:44Thank you!

Assignment Expert03.03.14, 13:02The 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.

JeeJa02.03.14, 14:42what is the probability that exactly one of them will solve it?

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Zia02.12.12, 13:22Very helpful

Assignment Expert14.10.11, 18:32We are pleased to help you

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sharmilla mohapatra12.05.11, 06:50Thanks a lot ur suggestion helped me solve my problem

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