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.

over the argument its not good to fight.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.