Samantha Is 1 Of 17 Students In A Class Of 85 Who Have Decided To Pursue A Business Degree. Each Week, A Student In The Class Is Randomly Selected To Tutor Younger Students. Choose The Letter For The Best Answer.1. What Is The Probability Of Drawing A
Introduction
Probability is a fundamental concept in mathematics that helps us understand the likelihood of events occurring. In real-life scenarios, probability is used to make informed decisions and predictions. In this article, we will explore a scenario where a student is randomly selected to tutor younger students, and we will calculate the probability of drawing a specific student.
The Scenario
Samantha is one of 17 students in a class of 85 who have decided to pursue a business degree. Each week, a student in the class is randomly selected to tutor younger students. We want to calculate the probability of drawing Samantha as the tutor.
Calculating Probability
To calculate the probability of drawing Samantha, we need to use the formula:
P(event) = Number of favorable outcomes / Total number of possible outcomes
In this case, the favorable outcome is drawing Samantha, and the total number of possible outcomes is the total number of students in the class.
Step 1: Identify the Number of Favorable Outcomes
The number of favorable outcomes is the number of students in the class who are pursuing a business degree and are eligible to be selected as tutors. Since Samantha is one of these students, the number of favorable outcomes is 1.
Step 2: Identify the Total Number of Possible Outcomes
The total number of possible outcomes is the total number of students in the class. In this case, there are 85 students in the class.
Step 3: Calculate the Probability
Now that we have identified the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability of drawing Samantha.
P(Samantha) = Number of favorable outcomes / Total number of possible outcomes = 1 / 85 = 0.0118 (or approximately 1.18%)
Conclusion
In conclusion, the probability of drawing Samantha as the tutor is approximately 1.18%. This means that if a student is randomly selected from the class, there is a 1.18% chance that Samantha will be selected.
Real-Life Applications
Probability is used in many real-life scenarios, including:
- Insurance: Insurance companies use probability to calculate the likelihood of an event occurring, such as a car accident or a natural disaster.
- Finance: Financial institutions use probability to calculate the likelihood of a stock or bond performing well.
- Medicine: Medical professionals use probability to calculate the likelihood of a patient responding to a treatment.
- Sports: Coaches and players use probability to calculate the likelihood of winning a game or a tournament.
Example Questions
- What is the probability of drawing a student who is not pursuing a business degree?
- What is the probability of drawing a student who is in the top 10% of the class?
- What is the probability of drawing a student who is in the bottom 10% of the class?
Answers
- The probability of drawing a student who is not pursuing a business degree is 1 - (Number of business students / Total number of students) = 1 - (17 / 85) = 0.9882 (or approximately 98.82%).
- The probability of drawing a student who is in the top 10% of the class is 0.1 (since 10% of 85 is 8.5, which is rounded to 10).
- The probability of drawing a student who is in the bottom 10% of the class is 0.1 (since 10% of 85 is 8.5, which is rounded to 10).
Conclusion
Frequently Asked Questions
Q: What is probability?
A: Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1 that represents the chance of an event happening.
Q: How is probability calculated?
A: Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Q: What is the difference between probability and chance?
A: Probability and chance are often used interchangeably, but they have slightly different meanings. Probability is a mathematical concept that represents the likelihood of an event occurring, while chance is a more general term that refers to the uncertainty of an event.
Q: What is the probability of an event that is certain to occur?
A: The probability of an event that is certain to occur is 1.
Q: What is the probability of an event that is impossible to occur?
A: The probability of an event that is impossible to occur is 0.
Q: What is the probability of an event that is equally likely to occur or not occur?
A: The probability of an event that is equally likely to occur or not occur is 0.5.
Q: Can probability be greater than 1?
A: No, probability cannot be greater than 1. If the probability of an event is greater than 1, it means that the event is certain to occur, and the probability should be 1.
Q: Can probability be less than 0?
A: No, probability cannot be less than 0. If the probability of an event is less than 0, it means that the event is impossible to occur, and the probability should be 0.
Q: What is the law of large numbers?
A: The law of large numbers states that as the number of trials increases, the average of the results will approach the expected value. In other words, the more trials you conduct, the closer the average of the results will be to the expected value.
Q: What is the concept of independent events?
A: Independent events are events that do not affect each other. The probability of one event occurring does not affect the probability of another event occurring.
Q: What is the concept of dependent events?
A: Dependent events are events that affect each other. The probability of one event occurring can affect the probability of another event occurring.
Q: What is the concept of conditional probability?
A: Conditional probability is the probability of an event occurring given that another event has occurred.
Q: What is the concept of Bayes' theorem?
A: Bayes' theorem is a mathematical formula that describes the relationship between conditional probabilities. It is used to update the probability of an event based on new information.
Q: What is the concept of probability distribution?
A: A probability distribution is a function that describes the probability of different values of a random variable.
Q: What is the concept of expected value?
A: The expected value is the average value of a random variable. It is calculated by multiplying each possible value of the variable by its probability and summing the results.
Q: What is the concept of variance?
A: The variance is a measure of the spread of a random variable. It is calculated by finding the average of the squared differences between each value of the variable and the expected value.
Q: What is the concept of standard deviation?
A: The standard deviation is a measure of the spread of a random variable. It is the square root of the variance.
Conclusion
In conclusion, probability is a fundamental concept in mathematics that has many real-world applications. It is used to describe the likelihood of events occurring and to make predictions about the future. We have answered many frequently asked questions about probability and provided explanations for each concept.