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	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 (square) (round to three decimal places as needed.)

Explanation:

Step1: Identify relevant values

Let \(A\) be the event of spending money and \(B\) be the event of being given four - quarters. The number of students given four quarters is \(29 + 19=48\). The number of students who were given four quarters and spent the money (purchased gum) is \(29\).

Step2: Apply conditional - probability formula

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In terms of counts, \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, \(n(A\cap B) = 29\) (students given four quarters and spent money) and \(n(B)=48\) (students given four quarters). So \(P(A|B)=\frac{29}{48}\approx0.604\).

Answer:

\(0.604\)