Coffee at Mom's Diner
Alignments to Content Standards:
S-CP.B.7
Task
At Mom’s diner, everyone drinks coffee. Let $C =$ the event that a randomly-selected customer puts cream in their coffee. Let $S =$ the event that a randomly-selected customer puts sugar in their coffee. Suppose that after years of collecting data, Mom has estimated the following probabilities:
$$
\begin{align}
&P(C)=0.6 \\
&P(S)=0.5 \\
&P(C \text{ or } S)=0.7
\end{align}
$$
Estimate $P(C \text{ and } S)$ and interpret this value in the context of the problem.
IM Commentary
This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context.
While the most obvious use of this task is as an assessment item, it could also be used in instruction as a proactice problem,
Solution
Using the addition rule, $P(C \text{ or } S) = P(C) + P(S) - P(C \text{ and } S)$, it follows that:
\begin{align}
0.7 &= 0.6 + 0.5 - P(C \text{ and } S) \\
P(C \text{ and } S) &= 0.6 + 0.5 - 0.7 \\
& = 0.4
\end{align}
The probability that a randomly-selected customer at Mom’s has both cream and sugar in his or her coffee is 0.4.
