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babunello [35]
3 years ago
13

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

m inspected?
Mathematics
1 answer:
labwork [276]3 years ago
6 0

Answer: The required probability is 0.1328.

Step-by-step 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.

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