In an experiment, college students were given either four quarters or a $\$ 1$ bill and they could either keep the money or spend it on gum. The results are summarized in the table.
\begin{tabular}{c|c|c}
\hline & Purchased Gum & Kept the Money \\
\hline Students Given Four Quarters & 35 & 14 \\
\hline Students Given a \$1 Bill & 18 & 28 \\
\hline
\end{tabular}
Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
A. 0.368
B. 0.714
C. 0.660
D. 0.391
Answer
\(\boxed{0.714}\) is the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
Step 1 ：Define the events: Let A be the event that a student spends the money and B be the event that the student was given four quarters.
Step 2 ：From the table, we find that the total number of students given four quarters is \(35 + 14 = 49\). This is the total number of outcomes for event B.
Step 3 ：The number of students who were given four quarters and spent the money is 35. This is the number of outcomes for both events A and B.
Step 4 ：Substitute these values into the formula for conditional probability: \(P(A|B) = P(A \cap B) / P(B) = 35 / 49\).
Step 5 ：Calculate the probability: \(P(A|B) = 35 / 49 = 0.714\).
Step 6 ：\(\boxed{0.714}\) is the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
