A Survey of an Introductory Statistics Class in Autumn 2003 $\quad\quad\quad\quad\quad\quad\quad\quad\text { Breakfast }$

A survey of an introductory statistics class in Autumn 2003 asked students whether or not they ate breakfast the morning of the survey. Results are as follows: $\quad\quad\quad\quad\quad\quad\quad\quad\text { Breakfast }$
$\text { Sex }\begin{array}{|c|c|c|c|}\hline & \text { Yes } & \text { No } & \text { Total } \\\hline \text { Male } & 66 & 66 & 132 \\\hline \text { Female } & 125 & 74 & 199 \\\hline \text { Total } & 191 & 140 & 331 \\\hline\end{array}$
a. What is the probability that a randomly selected student is female?
b. What is the probability that a randomly selected student ate breakfast?
c. What is the probability that a randomly selected student is a female who ate breakfast
d. What is the probability that a randomly selected student is female, given that the student
ate breakfast?
e. What is the probability that a randomly selected student ate breakfast, given that the student is female?
f. Does it appear that whether or not a student ate breakfast is independent of the student's sex? Explain.