Posted by **sc** on Thursday, May 3, 2012 at 8:43pm.

According to insurance records a car with a certain protection system will be recovered 89% of the time. Find the probability that 3 of 7 stolen cars will be recovered.

- Statistics -
**David Q/R**, Saturday, May 5, 2012 at 3:21pm
Use the binomial theorem. The probability that out of 7 stolen cars, the first three will be recovered is 0.89^3 x (1-0.89)^4 (because you also have to calculate the probability that the last four will NOT be recovered). That is 0.000103. But it's not just the first three that could have been recovered: you also have to work out in how many ways those three recovered ones could have been distributed among the seven, and multiply your answer by that. The number of ways it could have happened is (7!) / (3!)(4!)), where N! means N x (N-1) n (N-2) x ... 2 x 1. So the number of ways it could have happened is (7x6x5x4x3x2x1)/((4x3x2x1)x(3x2x1)), which is (7x6x5)/(3x2x1) = 35. Multiply that by the probability you worked out earlier, and you'll get 0.003613 - and that's your answer.

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