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 Four Quarters 27 16 Students Given a $1 Bill 12 35 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 (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 (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 spent 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 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.

	Purchased Gum	Kept the Money
Students Given Four Quarters	27	16
Students Given a $1 Bill	12	35

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
(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
(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 spent 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 kept the money.

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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 27 16
Students Given a1 Bill 12 35

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
(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 a1 bill.

The probability is
(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 a1 bill is more likely to have spent 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 a1 bill is more likely to have kept the money.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jason Horton

02/12/2023

Step 1

To find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill, we use the formula: P(spent money | given $1 bill) = (number of students who spent money and were given $1 bill) / (total number of students Show more…

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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 27 16 Students Given a $1 Bill 12 35 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 (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 (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 spent 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 kept the money.

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Transcript

00:01 In your question, you're given data from an experiment where students were either given four quarters or a dollar bill.

00:07 And then they were given the option to spend that money on gum or keep the money.

00:14 So the results are shown in the table.

00:16 What i would add to your table are totals.

00:19 I would add a total for the columns.

00:22 This will give me a 39 there and a 51 here.

00:26 I would add totals for the rows, which would give me 4 .4.

00:30 43 for the upper row and 47 for the second row.

00:39 And then you could total these, and you're going to end up with 90, no matter whether you look at that bottom row or you look at the columns.

00:49 So it always adds the totals into our calculations here.

00:55 Now, in part a, you're asked to do a conditional probability.

00:59 It is the probability that the randomly selected students spent the money conditioned on or given that we know they were given a $1 bill.

01:11 So the fact that we were given a $1 bill means we are only in the $1 bill row of this table.

01:19 None of the other information is of any concern because we are told, even for the second question, that we know the person we've picked, has been given a $1 bill.

01:33 So that means the denominators of our probability will just be the 47 for that row in both questions.

01:42 And then the probability of spent, that was the gum, purchased gum, that was 12, and the probability of keeping the money was 35 out of 47.

01:55 So that completes the probability part of your question.

01:59 So i'm going to highlight those in green, your answer for part a was 1247s, part b, 3547s.

02:10 Now, when you go to question c, it says, what does this probability suggest? what are those results that we just found suggest? if you look at those, there's two of the answers...

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