Question

Products produced by a machine has a 3% defective rate. What is the probability that the first defective occurs in the fifth item inspected?

Answer 1

Answer: The required probability is 0.1328.

Explanation:

Since we have given that

n = 5

Probability of success = p = defective rate = 3% = 0.03

Probability of failure = q = 1-p = 1 - 0.03 = 0.97

So, we will use "Binomial distribution":

probability that the first defective occurs in the fifth item inspected would be

`P(X=1)=^5C_1(0.03)^1(0.097)^4\\\\P(X=1)=0.1328`

Hence, the required probability is 0.1328.