Math

Question Experiment on college students given quarters or $1\$ 1 bill to keep or spend on gum. Find probabilities of spending or keeping the money and interpret the results.
a. Probability of spending $1\$ 1 bill: \square b. Probability of keeping $1\$ 1 bill: \square c. The results suggest: C. A student given a $1\$ 1 bill is more likely to have kept the money than a student given four quarters.

Studdy Solution

STEP 1

Assumptions
1. The table provided summarizes the results of the experiment accurately.
2. The probability is calculated as the number of favorable outcomes divided by the total number of outcomes in the given condition.
3. Rounding off the probability to three decimal places as required.

STEP 2

To find the probability of randomly selecting a student who spent the money, given that the student was given a $1\$ 1 bill, we need to calculate the ratio of the number of students who were given a $1\$ 1 bill and spent it on gum to the total number of students who were given a $1\$ 1 bill.
Probability=Number of students who spent the moneyTotal number of students given a $1 billProbability = \frac{\text{Number of students who spent the money}}{\text{Total number of students given a \$1 bill}}

STEP 3

From the table, we can see that the number of students who were given a $1\$ 1 bill and purchased gum is 13.

STEP 4

The total number of students given a $1\$ 1 bill is the sum of those who purchased gum and those who kept the money, which is 13 (purchased gum) + 33 (kept the money).
Totalnumberofstudentsgivena$1bill=13+33Total\, number\, of\, students\, given\, a\, \$1\, bill = 13 + 33

STEP 5

Calculate the total number of students given a $1\$ 1 bill.
Totalnumberofstudentsgivena$1bill=13+33=46Total\, number\, of\, students\, given\, a\, \$1\, bill = 13 + 33 = 46

STEP 6

Now, calculate the probability of a student spending the money given they were handed a $1\$ 1 bill.
Probability=1346Probability = \frac{13}{46}

STEP 7

Simplify the probability to a decimal and round to three decimal places.
Probability13460.283Probability \approx \frac{13}{46} \approx 0.283

STEP 8

For part b, we need to find the probability of randomly selecting a student who kept the money, given that the student was given a $1\$ 1 bill.
Probability=Number of students who kept the moneyTotal number of students given a $1 billProbability = \frac{\text{Number of students who kept the money}}{\text{Total number of students given a \$1 bill}}

STEP 9

From the table, we can see that the number of students who were given a $1\$ 1 bill and kept the money is 33.

STEP 10

We have already calculated the total number of students given a $1\$ 1 bill in STEP_5, which is 46.

STEP 11

Now, calculate the probability of a student keeping the money given they were handed a $1\$ 1 bill.
Probability=3346Probability = \frac{33}{46}

STEP 12

Simplify the probability to a decimal and round to three decimal places.
Probability33460.717Probability \approx \frac{33}{46} \approx 0.717

STEP 13

For part c, we need to interpret the results from parts a and b.
- From part a, we found that the probability of a student spending the money given they were handed a $1\$ 1 bill is approximately 0.283. - From part b, we found that the probability of a student keeping the money given they were handed a $1\$ 1 bill is approximately 0.717.

STEP 14

Comparing these probabilities, we can see that the probability of a student keeping the money (0.717) is greater than the probability of a student spending the money (0.283) when given a $1\$ 1 bill.

STEP 15

Therefore, the correct interpretation is option B: A student given a $1\$ 1 bill is more likely to have kept the money than to have spent the money.
The solution to the problem is:
a. The probability of randomly selecting a student who spent the money, given that the student was given a $1\$ 1 bill is 0.2830.283.
b. The probability of randomly selecting a student who kept the money, given that the student was given a $1\$ 1 bill is 0.7170.717.
c. The results suggest that a student given a $1\$ 1 bill is more likely to have kept the money than to have spent the money.

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