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 0.604
(round to three decimal places as needed.)
b. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
the probability is
(round to three decimal places as needed.)

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of a frequency - table, if we want to find the probability of event $A$ (spent the money) given event $B$ (given a $\$1$ bill), we use $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of students who were given a $\$1$ bill and spent the money, and $n(B)$ is the total number of students who were given a $\$1$ bill.

Step2: Identify relevant values from the table

The number of students who were given a $\$1$ bill and spent the money (purchased gum) is $n = 14$. The total number of students who were given a $\$1$ bill is $14 + 33=47$.

Step3: Calculate the probability

$P=\frac{14}{47}\approx0.298$

Answer:

$0.298$