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 25 17 Students Given a 1 Bill 14 34 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.)

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 25 17 Students Given a 1 Bill 14 34 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.)
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 & 25 & 17 \\ \hline Students Given a \$1 Bill & 14 & 34 \\ \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 $\square$ (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: Identify the row corresponding to the given condition

The row for the condition 'Students Given Four Quarters' is found.

Step 2: Sum the counts in this row to find the total occurrences under this condition

Total occurrences under the condition 'Students Given Four Quarters': 42

Step 3: Identify the count for the specific outcome under the given condition

Count for the outcome 'Purchased Gum' under the condition 'Students Given Four Quarters': 25

Step 4: Calculate the conditional probability

Conditional probability of 'Purchased Gum' given 'Students Given Four Quarters': 0.595

Step 5: Round the result

Rounded conditional probability: 0.595

Final Answer:

The conditional probability of 'Purchased Gum' given 'Students Given Four Quarters' is approximately 0.595.

Step 1: Identify the row corresponding to the given condition

The row for the condition 'Students Given Four Quarters' is found.

Step 2: Sum the counts in this row to find the total occurrences under this condition

Total occurrences under the condition 'Students Given Four Quarters': 42

Step 3: Identify the count for the specific outcome under the given condition

Count for the outcome 'Kept the Money' under the condition 'Students Given Four Quarters': 17

Step 4: Calculate the conditional probability

Conditional probability of 'Kept the Money' given 'Students Given Four Quarters': 0.405

Step 5: Round the result

Rounded conditional probability: 0.405

Final Answer:

The conditional probability of 'Kept the Money' given 'Students Given Four Quarters' is approximately 0.405.

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