Number of Students Who Spent Money

Oct 13, 2025 by pynkocean.com 78 views

The Coin Toss Experiment: A Study in Probability and Decision Making

In the field of mathematics, probability and decision making are two fundamental concepts that are often studied together. A classic experiment that illustrates the intersection of these two concepts is the coin toss experiment, also known as the "gambler's fallacy." In this experiment, participants are given a choice between two options: keeping a certain amount of money or spending it on a gamble. The results of the experiment can provide valuable insights into human decision making and the role of probability in shaping our choices.

In this 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 below:

Condition	Number of Students	Number of Students Who Spent Money	Percentage of Students Who Spent Money
Four Quarters	100	30	30%
$1 Bill	100	20	20%

Part (a)

What is the probability that a student will spend their money if they are given four quarters?

To solve this problem, we need to use the concept of conditional probability. Let's define the following events:

A: The student is given four quarters.
B: The student spends their money.

We want to find the probability of event B given that event A has occurred, denoted as P(B|A). Using the table, we can see that 30 out of 100 students who were given four quarters spent their money. Therefore, the probability of event B given that event A has occurred is:

P(B|A) = Number of students who spent money / Total number of students who received four quarters = 30/100 = 0.3

So, the probability that a student will spend their money if they are given four quarters is 0.3 or 30%.

Part (b)

What is the probability that a student will spend their money if they are given a $1 bill?

Using the same approach as in part (a), we can define the following events:

A: The student is given a $1 bill.
B: The student spends their money.

We want to find the probability of event B given that event A has occurred, denoted as P(B|A). Using the table, we can see that 20 out of 100 students who were given a $1 bill spent their money. Therefore, the probability of event B given that event A has occurred is:

P(B|A) = Number of students who spent money / Total number of students who received a $1 bill = 20/100 = 0.2

So, the probability that a student will spend their money if they are given a $1 bill is 0.2 or 20%.

Part (c)

What is the difference in probability between a student spending their money if they are given four quarters versus a $1 bill?

To solve this problem, we need to find the difference between the two probabilities calculated in parts (a) and (b). The difference in probability is:

Difference in probability = P(B|A) for four quarters - P(B|A) for $1 bill = 0.3 - 0.2 = 0.1

So, the difference in probability between a student spending their money if they are given four quarters versus a $1 bill is 0.1 or 10%.

In conclusion, the coin toss experiment provides valuable insights into human decision making and the role of probability in shaping our choices. The results of the experiment show that the probability of a student spending their money is higher if they are given four quarters (30%) compared to a $1 bill (20%). The difference in probability between the two conditions is 10%. These findings have implications for our understanding of decision making and the role of probability in shaping our choices.
Frequently Asked Questions: The Coin Toss Experiment

A: The coin toss experiment is a study in probability and decision making where participants are given a choice between two options: keeping a certain amount of money or spending it on a gamble. The results of the experiment can provide valuable insights into human decision making and the role of probability in shaping our choices.

A: In the 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 below:

Condition	Number of Students	Number of Students Who Spent Money	Percentage of Students Who Spent Money
Four Quarters	100	30	30%
$1 Bill	100	20	20%

A: The probability that a student will spend their money if they are given four quarters is 0.3 or 30%. This means that out of 100 students who were given four quarters, 30 students spent their money.

A: The probability that a student will spend their money if they are given a $1 bill is 0.2 or 20%. This means that out of 100 students who were given a $1 bill, 20 students spent their money.

A: The difference in probability between a student spending their money if they are given four quarters versus a $1 bill is 0.1 or 10%. This means that the probability of a student spending their money is 10% higher if they are given four quarters compared to a $1 bill.

A: The experiment provides valuable insights into human decision making and the role of probability in shaping our choices. The results of the experiment show that the probability of a student spending their money is higher if they are given four quarters compared to a $1 bill. This suggests that the value of the money and the perceived risk of the gamble can influence our decision making.

A: While the experiment provides valuable insights into human decision making, the results may not be generalizable to other situations. The experiment was conducted in a controlled environment with a specific population, and the results may not be representative of other populations or situations.

A: Some potential limitations of the experiment include:

The experiment was conducted with a specific population (college students) and may not be representative of other populations.
The experiment was conducted in a controlled environment and may not reflect real-world decision making.
The experiment only considered two options (keeping the money or spending it on gum) and may not reflect more complex decision making scenarios.

A: Some potential applications of the experiment include:

Understanding human decision making and the role of probability in shaping our choices.
Developing more effective decision making strategies.
Improving financial literacy and decision making skills.
Informing policy decisions related to financial education and decision making.