in an experiment, college students were given either four quarters or a $1 bill and they could either keep…

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.\n| students given four quarters | purchased gum | kept the money |\n| ---- | ---- | ---- |\n| 31 | 19 | |\n| students given a $1 bill | 16 | 26 |\n\na. find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.\nthe probability is (square) (round to three decimal places as needed.)\n\nb. find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.\nthe probability is (square) (round to three decimal places as needed.)\n\nc. what do the preceding results suggest?\na. a student given four quarters is more likely to have kept the money than a student given a $1 bill.\nb. a student given four quarters is more likely to have spent the money than a student given a $1 bill.\nc. a student given four quarters is more likely to have kept the money.\nd. a student given four quarters is more likely to have spent the money.

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.\n| students given four quarters | purchased gum | kept the money |\n| ---- | ---- | ---- |\n| 31 | 19 | |\n| students given a $1 bill | 16 | 26 |\n\na. find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.\nthe probability is (square) (round to three decimal places as needed.)\n\nb. find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.\nthe probability is (square) (round to three decimal places as needed.)\n\nc. what do the preceding results suggest?\na. a student given four quarters is more likely to have kept the money than a student given a $1 bill.\nb. a student given four quarters is more likely to have spent the money than a student given a $1 bill.\nc. a student given four quarters is more likely to have kept the money.\nd. a student given four quarters is more likely to have spent the money.

Answer

Explanation:

Step1: Define the formula for conditional probability

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

Step2: Calculate the probability of spending money given four quarters

The number of students given four quarters is $n = 31 + 19=50$. The number of students who were given four quarters and spent the money (purchased gum) is $31$. So the probability of randomly selecting a student who spent the money, given that the student was given four quarters is $P=\frac{31}{50}=0.62$.

Step3: Calculate the probability of keeping money given four quarters

The number of students who were given four quarters and kept the money is $19$. Using the same total number of students given four quarters ($n = 50$), the probability of randomly selecting a student who kept the money, given that the student was given four quarters is $P=\frac{19}{50}=0.38$.

Step4: Analyze the results

Since $0.62>0.38$, a student given four quarters is more likely to have spent the money.

Answer:

a. $0.62$ b. $0.38$ c. D. A student given four quarters is more likely to have spent the money.