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 GumKept the Money  Students Given Four Quarters33331515  Students Given a​ $1 Bill17173434 a. Find the probability of randomly selecting a student who spent the​ money, given that the student was given a​ $1 bill. The probability is nothing.​(Round to three decimal places as​ needed.)b. Find the probability of randomly selecting a student who kept the​ money, given that the student was given a​ $1 bill. The probability is nothing.​(Round to three decimal places as​ needed.)c. What do the preceding results​ suggest?  A.A student given a​ $1 bill is more likely to have kept the money than a student given four quarters. B.A student given a​ $1 bill is more likely to have kept the money. C.A student given a​ $1 bill is more likely to have spent the money than a student given four quarters. D.A student given a​ $1 bill is more likely to have spent the money.

Question
Asked Feb 21, 2019
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 Four Quarters
3333
1515
 
Students Given a $1 Bill
1717
3434
 
a. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
 
The probability is
nothing.
(Round to three decimal places as needed.)
b. Find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
 
The probability is
nothing.
(Round to three decimal places as needed.)
c. What do the preceding results suggest?
 
 
A.
A student given a $1 bill is more likely to have kept the money than a student given four quarters.
 
B.
A student given a $1 bill is more likely to have kept the money.
 
C.
A student given a $1 bill is more likely to have spent the money than a student given four quarters.
 
D.
A student given a $1 bill is more likely to have spent the money.
check_circle

Expert Answer

Step 1

Let, 

S = Event representing when student spend the money

M =  Event representing when student kept the money

Q = Event representing when student was given four quarters

B = Event representing when student was given $1 Bill

 Thus, we can reframe the table as shown;

 

 

S

K

Total

Q

33

15

48

B

17

34

51

Total

50

49

99

 

Step 2

From tha table we can calculate the shown probabilities ;

 

fullscreen
Step 3

a.   The probability of randomly selecting a student who spent the​ money, given that the student was given a​ $1 bill is given as;

P(S|B) 

which is the conditional probability.

Now lets apply the formula to calculate conditional probability and calculate P(S|B...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: What’s the mean annual return of the S&P 400 Midcap Index over the past 7 years?  What’s the sta...

A: Hello there! there are more than three sub parts in the given question. According to our policies we...

question_answer

Q: A political candidate has asked you to conduct a poll to determine what percentage of people support...

A: As there is no any estimates available, the sample proportion is assumed to be 0.50, that is, 50%.He...

question_answer

Q: The following joint probability distribution summarize the doctoral degrees conferred in the social ...

A: In this question, a table has given to us which shows the joint probability distribution, based on w...

question_answer

Q: Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). T...

A: Confidence interval when population standard deviation is not known:The formula of confidence interv...

question_answer

Q: The standard treatment for a disease works in 0.65 of all patients. A new treatment is patients (of ...

A: (a)The provided details are:

question_answer

Q: An economist is studying the job market in Denver area neighborhoods. Let x represent the total numb...

A: Scatter PlotIt is a Graph between two variables. It is plotted to check the relationship between the...

question_answer

Q: What determines whether a post hoc test is used in a one-way ANOVA calculation? Be specific.

A: ANOVA is generally used to analyze the  significant differences among group means. Here we apply F-t...

question_answer

Q: What percentage of hospitals provide at least some charity care? Based on a random sample of hospita...

A: Finding the mean and standard deviation of the variable X.Mean:The general formula to obtain the mea...

question_answer

Q: Statistics Question

A: According to the provided information, the variable ‘x’ be age of the best actress winner and ‘y’ be...