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	29

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

The number of students given four - quarters who spent the money (purchased gum) is 75, and the total number of students given four - quarters is \(75 + 14=89\).

Step2: Calculate the conditional probability

The formula for conditional probability \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, event \(A\) is spending the money and event \(B\) is being given four - quarters. So the probability \(P=\frac{75}{89}\approx0.843\).

Answer:

0.843