# What is the Correct Probability of a Student Becoming Chairperson?

• Shawn Garsed
I think the book may have an error.In summary, the question asks for the probability of a student being chosen as the chairperson out of a group of 4 students out of a total of 12 students. The correct answer is 1/12, while the book may have an error stating 1/2970 as the answer.
Shawn Garsed

## Homework Statement

A. Mrs. Moyer’s class has to choose 4 out of 12 people to serve on an activity
committee.
B. The four chosen students are then selected for the positions of chairperson, activities

What is the probability that anyone of the students is chosen to be the
chairperson?

## Homework Equations

Permutations and combinations

## The Attempt at a Solution

I first calculated the number of outcomes for part A: 12!/((12-4)!4!)=495. Then I calculated the number of outcomes for part B: 4!=24. Which gives the total number of outcomes: 495*24=11880.

After that, I calculated the favorable number of outcomes for A and B:

A: (1*11*10*9)/3!=165

B: 1*3*2*1=6

Which gives the total number of outcomes: 165*6=990.

Therefore, the probality is 990/11880 or 1/12.
The problem is that the book says it's 1/2970.

Who's right?

Shawn

Are you quite sure that's the question being asked?

As you've phrased the question, it has to be 1/12 because part A is irrelevant, all students have equal chance of being the chairperson.

That's exactly how the question is phrased. I even calculated it in different ways, the simplest being: 4 out of 12 means you have a 4/12 or 1/3 chance of being chosen and the chance of being chosen as chairperson is 1/4. (1/3)*(1/4)=1/12.

Last edited:
Well you are right about there being 1180 different combinations of 4 students. 2970 is a quarter of 1180 so it's not a totally random number but it definitely isn't the answer to your question.

## 1. What is probability?

Probability is a mathematical concept that measures the likelihood of an event occurring. It is often represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

## 2. How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you want to find the probability of rolling a 4 on a six-sided die, the calculation would be 1 favorable outcome (rolling a 4) divided by 6 possible outcomes (rolling any number from 1 to 6), resulting in a probability of 1/6 or approximately 0.17.

## 3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from repeated trials and may vary from the theoretical probability.

## 4. How can I apply probability in real-life situations?

Probability can be applied in various real-life situations such as weather forecasting, stock market analysis, and risk assessment in insurance. It can also be used to make predictions and informed decisions based on the likelihood of different outcomes.

## 5. What is the role of probability in statistics?

Probability is a fundamental concept in statistics and is used to analyze and interpret data. It helps in making inferences and drawing conclusions about a population based on a sample. Probability also allows for the calculation of confidence intervals and determining the significance of results in statistical tests.

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