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| | purchased gum | kept the money |\n|--|--|--| \n| students given four quarters | 25 | 14 |\n| students given a $1 bill | 16 | 35 |\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 0.641 (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 0.359 (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 spent the money than a student given a $1 bill.\nb. a student given four quarters is more likely to have spent the money.\nc. a student given four quarters is more likely to have kept the money than a student given a $1 bill.\nd. a student given four quarters is more likely to have kept 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| | purchased gum | kept the money |\n|--|--|--| \n| students given four quarters | 25 | 14 |\n| students given a $1 bill | 16 | 35 |\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 0.641 (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 0.359 (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 spent the money than a student given a $1 bill.\nb. a student given four quarters is more likely to have spent the money.\nc. a student given four quarters is more likely to have kept the money than a student given a $1 bill.\nd. a student given four quarters is more likely to have kept the money.

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequency, if we want to find the probability of event $A$ given event $B$, we use $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.

Step2: Calculate part (a)

For part (a), the number of students given four - quarters is $n = 25 + 14=39$. The number of students who spent the money (purchased gum) among those given four - quarters is $n_1 = 25$. So the probability $P=\frac{25}{39}\approx0.641$.

Step3: Calculate part (b)

For part (b), the number of students given four - quarters is still $n = 25+14 = 39$. The number of students who kept the money among those given four - quarters is $n_2 = 14$. So the probability $P=\frac{14}{39}\approx0.359$.

Step4: Analyze part (c)

The probability that a student given four - quarters spent the money is approximately $0.641$, and the probability that a student given a $$1$ bill spent the money is $\frac{16}{16 + 35}=\frac{16}{51}\approx0.314$. Since $0.641>0.314$, a student given four - quarters is more likely to have spent the money.

Answer:

a. $0.641$ b. $0.359$ c. B. A student given four quarters is more likely to have spent the money