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. Complete parts (a) through (c) below. \begin{tabular}{c|c|c} \hline & Purchased Gum & Kept the Money \\ \hline Students Given Four Quarters & 26 & 18 \\ \hline Students Given a \$1 Bill & 12 & 31 \\ \hline \end{tabular} a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. The probability is (Round to three decimal places as needed.) b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters. The probability is (Round to three decimal places as needed.) c. What do the preceding results suggest? A. A student given four quarters is more likely to have kept the money. R. A ctuident niven fnur nularters is more likelv tn have kent the monev than a ctuident niven a $\$ 1$ hill
Solution
Step 1 ：Given that the number of students who were given four quarters and spent the money is 26, and the number of students who kept the money is 18. The total number of students who were given four quarters is 44.
Step 2 ：To find the probability of a student spending the money given that they were given four quarters, we divide the number of students who spent the money and were given four quarters by the total number of students who were given four quarters. This gives us \(\frac{26}{44} = 0.591\)
Step 3 ：To find the probability of a student keeping the money given that they were given four quarters, we divide the number of students who kept the money and were given four quarters by the total number of students who were given four quarters. This gives us \(\frac{18}{44} = 0.409\)
Step 4 ：Final Answer: The probability of randomly selecting a student who spent the money, given that the student was given four quarters is approximately \(\boxed{0.591}\). The probability of randomly selecting a student who kept the money, given that the student was given four quarters is approximately \(\boxed{0.409}\).
Step 5 ：The preceding results suggest that a student given four quarters is more likely to spend the money than to keep it.
