Questions: 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. Purchased Gum Kept the Money --------- Students Given Four Quarters 34 11 Students Given a 1 Bill 15 29 a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. The probability is 0.756 . (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.)

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. Purchased Gum Kept the Money --------- Students Given Four Quarters 34 11 Students Given a 1 Bill 15 29 a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. The probability is 0.756 . (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.)
Transcript text: 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 & 34 & 11 \\ \hline Students Given a \$1 Bill & 15 & 29 \\ \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 0.756 . (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 $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Total Students Given Four Quarters

The total number of students who were given four quarters is calculated as follows:

\[ \text{Total Students Given Quarters} = \text{Purchased Gum} + \text{Kept the Money} = 34 + 11 = 45 \]

Step 2: Calculate the Probability of Spending the Money Given Four Quarters

The probability of a student spending the money, given that they were given four quarters, is calculated using the formula:

\[ P(\text{Spent} | \text{Quarters}) = \frac{\text{Purchased Gum}}{\text{Total Students Given Quarters}} = \frac{34}{45} \approx 0.756 \]

Step 3: Calculate the Probability of Keeping the Money Given Four Quarters

The probability of a student keeping the money, given that they were given four quarters, is calculated as follows:

\[ P(\text{Kept} | \text{Quarters}) = \frac{\text{Kept the Money}}{\text{Total Students Given Quarters}} = \frac{11}{45} \approx 0.244 \]

Final Answer

The probabilities are:

  • The probability of spending the money given four quarters is \( \boxed{0.756} \).
  • The probability of keeping the money given four quarters is \( \boxed{0.244} \).
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