# 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 GumKept the Money  Students Given Four Quarters33331515  Students Given a​ \$1 Bill17173434 a. Find the probability of randomly selecting a student who spent the​ money, given that the student was given a​ \$1 bill. The probability is nothing.​(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 a​ \$1 bill. The probability is nothing.​(Round to three decimal places as​ needed.)c. What do the preceding results​ suggest?  A.A student given a​ \$1 bill is more likely to have kept the money than a student given four quarters. B.A student given a​ \$1 bill is more likely 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 given a​ \$1 bill is more likely to have spent the money.

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 3333 1515 1717 3434
a. Find the probability of randomly selecting a student who spent the money, given that the student was given a \$1 bill.

The probability is
nothing.
(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 a \$1 bill.

The probability is
nothing.
(Round to three decimal places as needed.)
c. What do the preceding results suggest?

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

B.
A student given a \$1 bill is more likely 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 given a \$1 bill is more likely to have spent the money.
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Step 1

Let,

S = Event representing when student spend the money

M =  Event representing when student kept the money

Q = Event representing when student was given four quarters

B = Event representing when student was given \$1 Bill

Thus, we can reframe the table as shown;

 S K Total Q 33 15 48 B 17 34 51 Total 50 49 99

Step 2

From tha table we can calculate the shown probabilities ;

Step 3

a.   The probability of randomly selecting a student who spent the​ money, given that the student was given a​ \$1 bill is given as;

P(S|B)

which is the conditional probability.

Now lets apply the formula to calculate conditional probability and calculate P(S|B...

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