Fifteen cars are inspected for California emissions compliance. Twelve were found to be compliant and 3 were not. A sample of 7 cars is chosen at random. What is the probability that all 7 cars chosen are compliant?

Where N=15 is the population size, M=12 is the number of success states in the population, n=7 is the number of draws, k is the number of observed successes  

And using the probability mass function we got:

So then the answer for this case would be 0.123.

Step-by-step explanation:

Previous concepts

The hypergeometric distribution is a discrete probability distribution that its useful when we have more than two distinguishable groups in a sample and the probability mass function is given by:

Where N=15 is the population size, M=12 is the number of success states in the population, n=7 is the number of draws, k is the number of observed successes  

The expected value and variance for this distribution are given by:

Solution to the problem

For this case we want this probability:

And using the probability mass function we got:

So then the answer for this case would be 0.123.

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