# Thread: probability by first principles

1. ## 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

2. Originally Posted by renlok
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).