Afactory 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?

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) =

P(X=0) =

Using n=30 and p=0.04

P(X=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