Question

A factory tests a random sample of 30 transistors for defects. the probability that a particular transistor will be defective has been established by past experience as 0.04. what is the probability that there are no defective transistors in the​ sample?

Answer 1

Let X be the number of defective transistors. Let p be the probability that defective transistor.

P(defective transistor) = 0.04

P(non defective ) = 1- 0.04 = 0.96

A random sample of size 30 is tested for defects and we want to find probability of no defective transistor

P(No defective transistor) = P(X= 0)

Here X follows binomial distribution with parameters n=30 and p=0.04

The Binomial probability function with parameters n and p is

P(X=x) = $(nCx) p^{x} (1-p)^{n-x}$

P(X=0) = $(nC0) p^{0} (1-p)^{n-0}$

Using n=30 and p=0.04

P(X=0) = $(30C0) 0.04^{0} (1-0.04)^{30-0}$

P(X=0) = 1*1*(0.96)^30

P(X=0) = 0.2938

The probability that there are no defective transistors in the sample is 0.2938