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 Four Quarters	35	17
Students Given a​ $1 Bill	19	30

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 kept the money.

C.

A student given four quarters is more likely to have spent the money than a student given a​ $1 bill.

D.

A student given four quarters is more likely to have spent the money.

Answer 1

The completed table is as below

	Purchased Gum	Kept the money	Total
Given 4 quarters	35	17	52
Given a dollar	19	30	49
Total	54	47	101

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(a) P(Selecting a student who spent the money given that the student was given 4 quarters)

= P(Spent/4 Quarters)

By Bayes Theorem, P(A/B) = P(A and B)/P(B). Therefore

P(Spent/4 Quarters) = P(Spent and 4 quarters)/P(4 quarters) = (35/101) / (52/101) = 35/52 = 0.673

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(b) P(Selecting a student who kept the money given that the student was given 4 quarters)

= P(Kept/4 Quarters)

By Bayes Theorem, P(A/B) = P(A and B)/P(B). Therefore

P(Kept/4 Quarters) = P(Kept and 4 quarters)/P(4 quarters) = (47/101) / (52/101) = 35/54 = 0.904

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(c) From the results in (a) and (b) A student given 4 quarters has a higher probability of keeping it (0.904) than having spent it (0.673). Therefore OPTION B.

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