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Math Help - probability by first principles

  1. #1
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    probability by first principles

    I have the question
    A proportion p of all trucks passing a busy motorway exit point have faulty brakes. An inspector inspects 8 trucks randomly from passing this point. Find from "first principles" that 6 of the trucks have faulty brakes
    first off i dont really know what first principles is but i know the probability is just p6/8 i just dont how to get this vis first principles
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  2. #2
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    Quote Originally Posted by renlok View Post
    I have the question


    first off i dont really know what first principles is but i know the probability is just p6/8 i just dont how to get this vis first principles
    Assuming that the population of trucks that the 8 have been chosen from is large, the answer is {8 \choose 6} p^6 (1 - p)^2. (You should review the derivation of the binomial distribution).
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