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?

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

step-by-step 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

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