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	35

a. find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
the probability is 0.841
(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.)

Explanation:

Step1: Identify relevant values

The number of students given four - quarters is \(75 + 14=89\). The number of students given four - quarters who kept the money is 14.

Step2: Calculate the conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the case of frequency data, if \(A\) is the event of keeping the money and \(B\) is the event of being given four - quarters, the probability \(P=\frac{\text{Number of students who kept money and were given four - quarters}}{\text{Number of students given four - quarters}}\). So \(P=\frac{14}{89}\approx0.157\).

Answer:

0.157