At the University of Tough Love, Good Grades in Math

Essay

At the University of Tough Love, good grades in math are hard to come by. The
grade distribution is shown in the table below: $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Grade } & \mathbf { A } & \mathbf { B } & \mathbf { C } & \mathbf { D } & \mathbf { F } \\\hline \text { Proportion } & 0.10 & 0.15 & 0.35 & 0.35 & 0.05 \\\hline\end{array}$$ Suppose three students' grade reports are selected at random with replacement. (The
math grade is written down and the report replaced in the population of reports before
the next report is selected.) Three possible outcomes of this experiment are listed
below. Calculate the probabilities of these sequences appearing. a) $\mathbf { A B C }$
b) $C C D$