Question $1$: A smog alert has been called in a certain area of Izmir in which there are several industrial

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firms. An inspector will visit $10$ randomly selected firms to check for violations of regulations. Let X

be the number of firms visited by the inspector that are in violation.

a$.$ If there are $50$ industrial firms in the area of which $15$ are in violation, what is the probability mass

function of $x?$

b$.$ If there are $500$ firms in the area of which $150$ are in violation, write an exact expression for and

propose an approximation.