Question

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)

	purchased gum	kept the money
students given a $1 bill	14	33

a. find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. the probability is 0.604 (round to three decimal places as needed.)
b. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill. the probability is 0.298 (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 spent the money than a student given a $1 bill
b. a student was more likely to have spent the money than to have kept the money
c. a student given a $1 bill is more likely to have spent the money than a student given four quarters
d. a student was more likely to be given four quarters than a $1 bill

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of frequency - tables, if $A$ is the event of spending money and $B$ is the event of being given a certain form of money, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.

Step2: Calculate part (a)

For students given four quarters, the number of students given four quarters is $n = 29 + 19=48$. The number of students who spent the money (purchased gum) among those given four quarters is $29$. So the probability $P=\frac{29}{48}\approx0.604$.

Step3: Calculate part (b)

For students given a $\$1$ bill, the number of students given a $\$1$ bill is $n = 14+33 = 47$. The number of students who spent the money (purchased gum) among those given a $\$1$ bill is $14$. So the probability $P=\frac{14}{47}\approx0.298$.

Step4: Analyze part (c)

Since $0.604>0.298$, a student given four quarters is more likely to have spent the money than a student given a $\$1$ bill.

Answer:

a. $0.604$
b. $0.298$
c. A. A student given four quarters is more likely to have spent the money than a student given a $\$1$ bill