Question

Products produced by a certain machine has 15% defective rate.

What is the probability that the first defective item occurs in the first 12 inspections?

Answer 1

The probability that the first defective item occurred in the first 12 inspection is 0.3012

Explanation:

This is a binomial distribution question;

P= 0.15 (prob of success)

q=1-p, q= 1- 0.15= 0.85

n= 12 x= 1

Using the binomial formula

P(x=1) = nCx P^x q ^ n-x

= 12C1 (0.15)^1 (0.85)^ 12-1

= 12 × 0.15 × (0.85)^11

= 0.3012

See attached picture