Unit 5: Modeling with Probability

Overview

Life is full of uncertainty and risks. Based on the predictions of weather forecasters, we decide what to wear and whether to carry an umbrella. We buy car insurance to compensate us in the event of an accident. We buy life insurance to help us take care of our families in the event of our untimely demise. Stock market investments are made based on the probability of a businesses future performance. Probability theory is the “mathematics of risk and uncertainty” and it gives us a way to look into the future of probable events, enabling us to see into the unknown. Thus, we can use expected value and probability distributions to help make decisions that affect our future. For example, should you spend $50 a year for an insurance policy that pays $150,000 if you become too sick to finish your college education? Or, theoretically is there anything to gain or lose by guessing on a multiple-choice test that has four possible answers? What if you only want to buy a lottery ticket if your expected winnings are larger than the ticket price? If tickets are $4, prize is $1500, and the odds of winning are 1 in 400, meaning that the probability of winning is 1/400. Should you buy a ticket? How do insurance companies in the business to make money set the premium amounts based on the age and sex of the drivers? All of these real-life examples use expected value and probability theory to peek into the future and make decisions based on what the numbers say. Expected value, using probabilities, is a mathematical way to determine what to expect in various situations over the long run.

 

 

Developed By: Sandra Kelly


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Pre-Unit Assessment

Lesson 1

Random Variables, Discrete Probability Distribution Tables, and Expected Value

Post-Unit Assessment