Question

a random sample of 4 claims are selected from a lot of 12 that has 3 nonconforming units. using the hypergeometric distribution what is the probability that the sample will contain exactly 0 nonconforming units? 1 non conforming unit

Answer 1

The probability that the sample will contain exactly 0 nonconforming units is P=0.25.

The probability that the sample will contain exactly 1 nonconforming units is P=0.51.

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Explanation:

We have a sample of size n=4, taken out of a lot of N=12 units, where K=3 are non-conforming units.

We can write the probability mass function as:

`P(x=k)=\frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}`

where k is the number of non-conforming units on the sample of n=4.

We can calculate the probability of getting no non-conforming units (k=0) as:

`P(x=0)=\frac{\binom{3}{0}\binom{9}{4}}{\binom{12}{4}}=(1*126)/(495)=(126)/(495) = 0.25`

We can calculate the probability of getting one non-conforming units (k=1) as:

`P(x=1)=\frac{\binom{3}{1}\binom{9}{3}}{\binom{12}{4}}=(3*84)/(495)=(252)/(495) = 0.51`