A Statistics Professor Classifies His Students According to Their Gender

Essay

A statistics professor classifies his students according to their gender and the number of hours of paid work they do a week. The following table gives the proportions of students falling into the various categories. One student is selected at random.
Paid Work (hours/week) $$\begin{array} { | l | c | c | c | c | } \hline \text { Gender } & 0 & 1 - 8 & 9 - 16 & \text { Over } 16 \\\hline \text { Male } & 0.06 & 0.20 & 0.15 & 0.06 \\\hline \text { Female } & 0.12 & 0.18 & 0.20 & 0.03 \\\hline\end{array}$$ a. If the student selected is female, what is the probability that he works between 1 and 8 hours a week?
b. If the selected student works more than 16 hours a week, what is the probability that the student is male?
c. What is the probability that the student selected is female or does do any paid work or both?
d. Is gender independent of the number of hours of paid work done a week? Explain using probabilities.