In an experiment, college students were given either four quarters or à $1 bill and they could either keep the money or spend it on gum. The res the table. Complete parts (a) through (c) below. Purchased Gum Students Given Four Quarters Students Given a $1 Bill Kept the Money 14 25 18 31 a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
In an experiment, college students were given either four quarters or à $1 bill and they could either keep the money or spend it on gum. The res the table. Complete parts (a) through (c) below. Purchased Gum Students Given Four Quarters Students Given a $1 Bill Kept the Money 14 25 18 31 a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![### College Students' Behavior with Different Denominations in a Spending Experiment
**Scenario:**
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 presented in the table below. Complete parts (a) through (c) according to the given data.
**Data Table:**
| Group | Purchased Gum | Kept the Money |
|--------------------------------------|---------------|----------------|
| Students Given Four Quarters | 25 | 14 |
| Students Given a $1 Bill | 18 | 31 |
**Questions:**
**a.** Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
*Formula:* \( \text{Probability} = \frac{\text{Number of students who purchased gum with four quarters}}{\text{Total number of students given four quarters}} \)
The probability is: **\[ \square \]**
(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 four quarters.
*Formula:* \( \text{Probability} = \frac{\text{Number of students who kept the money with four quarters}}{\text{Total number of students given four quarters}} \)
The probability is: **\[ \square \]**
(Round to three decimal places as needed.)
---
**c.** What do the preceding results suggest?
- **A.** A student given four quarters is more likely to have spent the money.
- **B.** A student given four quarters is more likely to have spent the money than a student given a $1 bill.
- **C.** A student given four quarters is more likely to have kept the money.
- **D.** A student given four quarters is more likely to have kept the money than a student given a $1 bill.
---
### Explanation of Graphs and Interpretation:
The table provides clear categories and numerical data about students’ choices when given different denominations. By calculating the given probabilities, students can derive meaningful insights about spending behavior based on the type of denomination received. The interpretations from these results help in understanding underlying financial decision-making tendencies among students.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05e4ecee-2cea-4f4d-ab25-0174354ce1c3%2Fdc9f1998-ea19-4838-b4fe-a255f3c9578f%2F1how5n.jpeg&w=3840&q=75)
Transcribed Image Text:### College Students' Behavior with Different Denominations in a Spending Experiment
**Scenario:**
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 presented in the table below. Complete parts (a) through (c) according to the given data.
**Data Table:**
| Group | Purchased Gum | Kept the Money |
|--------------------------------------|---------------|----------------|
| Students Given Four Quarters | 25 | 14 |
| Students Given a $1 Bill | 18 | 31 |
**Questions:**
**a.** Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
*Formula:* \( \text{Probability} = \frac{\text{Number of students who purchased gum with four quarters}}{\text{Total number of students given four quarters}} \)
The probability is: **\[ \square \]**
(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 four quarters.
*Formula:* \( \text{Probability} = \frac{\text{Number of students who kept the money with four quarters}}{\text{Total number of students given four quarters}} \)
The probability is: **\[ \square \]**
(Round to three decimal places as needed.)
---
**c.** What do the preceding results suggest?
- **A.** A student given four quarters is more likely to have spent the money.
- **B.** A student given four quarters is more likely to have spent the money than a student given a $1 bill.
- **C.** A student given four quarters is more likely to have kept the money.
- **D.** A student given four quarters is more likely to have kept the money than a student given a $1 bill.
---
### Explanation of Graphs and Interpretation:
The table provides clear categories and numerical data about students’ choices when given different denominations. By calculating the given probabilities, students can derive meaningful insights about spending behavior based on the type of denomination received. The interpretations from these results help in understanding underlying financial decision-making tendencies among students.
![### Probability Calculations Using a Standard Deck of Cards
**Problem Statement:**
A standard deck of cards contains 52 cards. One card is selected from the deck.
**Questions:**
(a) Compute the probability of randomly selecting a two or seven.
(b) Compute the probability of randomly selecting a two or seven or four.
(c) Compute the probability of randomly selecting a king or spade.
**Solutions:**
(a) \( P(\text{two or seven}) = \)
(Type an integer or a decimal rounded to three decimal places as needed.)
(b) \( P(\text{two or seven or four}) = \)
(Type an integer or a decimal rounded to three decimal places as needed.)
(c) \( P(\text{king or spade}) = \)
(Type an integer or a decimal rounded to three decimal places as needed.)
### Explanation:
(a) To find \( P(\text{two or seven}) \):
- A standard deck has 4 twos and 4 sevens.
- Total favorable outcomes = 4 (twos) + 4 (sevens) = 8.
- Total possible outcomes = 52.
\[ P(\text{two or seven}) = \frac{8}{52} = 0.154 \] (rounded to three decimal places)
(b) To find \( P(\text{two or seven or four}) \):
- A standard deck has 4 twos, 4 sevens, and 4 fours.
- Total favorable outcomes = 4 (twos) + 4 (sevens) + 4 (fours) = 12.
- Total possible outcomes = 52.
\[ P(\text{two or seven or four}) = \frac{12}{52} = 0.231 \] (rounded to three decimal places)
(c) To find \( P(\text{king or spade}) \):
- A standard deck has 4 kings.
- There are 13 spades.
- One of the spades is a king, which means there is double-counting for that king.
- Total unique favorable outcomes = 4 (kings) + 12 (remaining spades) = 16.
- Total possible outcomes = 52.
\[ P(\text{king or spade}) = \frac{16}{52} = 0.308 \] (rounded to three decimal places)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05e4ecee-2cea-4f4d-ab25-0174354ce1c3%2Fdc9f1998-ea19-4838-b4fe-a255f3c9578f%2Fr2q28st.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Calculations Using a Standard Deck of Cards
**Problem Statement:**
A standard deck of cards contains 52 cards. One card is selected from the deck.
**Questions:**
(a) Compute the probability of randomly selecting a two or seven.
(b) Compute the probability of randomly selecting a two or seven or four.
(c) Compute the probability of randomly selecting a king or spade.
**Solutions:**
(a) \( P(\text{two or seven}) = \)
(Type an integer or a decimal rounded to three decimal places as needed.)
(b) \( P(\text{two or seven or four}) = \)
(Type an integer or a decimal rounded to three decimal places as needed.)
(c) \( P(\text{king or spade}) = \)
(Type an integer or a decimal rounded to three decimal places as needed.)
### Explanation:
(a) To find \( P(\text{two or seven}) \):
- A standard deck has 4 twos and 4 sevens.
- Total favorable outcomes = 4 (twos) + 4 (sevens) = 8.
- Total possible outcomes = 52.
\[ P(\text{two or seven}) = \frac{8}{52} = 0.154 \] (rounded to three decimal places)
(b) To find \( P(\text{two or seven or four}) \):
- A standard deck has 4 twos, 4 sevens, and 4 fours.
- Total favorable outcomes = 4 (twos) + 4 (sevens) + 4 (fours) = 12.
- Total possible outcomes = 52.
\[ P(\text{two or seven or four}) = \frac{12}{52} = 0.231 \] (rounded to three decimal places)
(c) To find \( P(\text{king or spade}) \):
- A standard deck has 4 kings.
- There are 13 spades.
- One of the spades is a king, which means there is double-counting for that king.
- Total unique favorable outcomes = 4 (kings) + 12 (remaining spades) = 16.
- Total possible outcomes = 52.
\[ P(\text{king or spade}) = \frac{16}{52} = 0.308 \] (rounded to three decimal places)
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