Chapter 3.6, Problem 1E

In Example 1, we wrote, “the probability that a response is yes, given that it is from a man” as $p\left(Y|M\right)$, we wrote, “the probability that a response is yes and is from a man” as $p\left(Y\cap M\right)$. In Exercise 1-4, write the given probabilities in a similar manner. Also, identify which are conditional and which are not conditional.

Let $H$ be the event that a job candidate is hired, and let $Q$ be the event that a job candidate is well qualified. Use the symbols $H$, $Q$, $|$ and $\cap$ to write the following probabilities.

a. The probability that a job candidate is hired given that the candidate is well qualified.

b. The probability that a job candidate is hired and the candidate is well qualified.