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) below.

	purchased gum	kept the money
students given a $1 bill	16	25

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 than a student given a $1 bill
b. a student given four quarters is more likely to have spent the money than a student given a $1 bill.
c. a student given four quarters is more likely to have kept the money
d. a student given four quarters is more likely to have spent the money

Explanation:

Step1: Calculate total students given four - quarters

The total number of students given four quarters is \(33 + 19=52\).

Step2: Calculate probability of spending money given four - quarters

The number of students who spent money (purchased gum) and were given four quarters is 33. The probability \(P(\text{spent}|\text{four quarters})\) is \(\frac{33}{52}\approx0.635\).

Step3: Calculate probability of keeping money given four - quarters

The number of students who kept money and were given four quarters is 19. The probability \(P(\text{kept}|\text{four quarters})\) is \(\frac{19}{52}\approx0.365\).

Step4: Analyze the results

The probability that a student given four quarters spent the money (\(0.635\)) is higher than the probability that a student given a \(\$1\) bill spent the money (\(\frac{16}{16 + 25}=\frac{16}{41}\approx0.390\)).

Answer:

a. \(0.635\)
b. \(0.365\)
c. B. A student given four quarters is more likely to have spent the money than a student given a \(\$1\) bill.