A manufacturing machine has a 3% defect rate. If 4 items

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A manufacturing machine has a 3% defect rate. If 4 items

Nann 2021-09-15 Answered

A manufacturing machine has a 3% defect rate.
If 4 items are chosen at random, what is the probability that at least one will have a defect?

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Expert Answer

sweererlirumeX

Answered 2021-09-16 Author has 91 answers

Step 1
Here, X denotes that the item is defective, which follows binomial distribution with

n = 4 Z K S and P S K p = 0.03

.
The formula to find the binomial probability is,

P (X = x) =^{n} C_{x} p^{x} {(1 - p)}^{(n - x)}

Step 2
Probability that at least one will have a defect:
The probability that at least one will have a defect is,

P (X \geq 1) = 1 - P (X = 0)

= 1 -^{4} C_{0} {(0.03)}^{0} {(1 - 0.03)}^{(4 - 0)}

= 1 - 0.8853

= 0.1147

The probability that at least one will have a defect is 0.1147.

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