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MDM4U-B Binomial and Hypergeometric Probability Distributions 15

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Mathematics of Data Management MDM4U-B Lesson 15 1 Introduction In this lesson, you will explore both binomial and hypergeometric distributions. You will learn how to distinguish between the two distributions by analyzing the characteristics of a given question and seeing how they can be applied to solving real-life problems. Planning Your Study You may find this time grid helpful in planning when and how you will work through this lesson. Suggested Timing for This Lesson (Hours) Binomial Probability Distributions 1 Expected Value and the Binomial Distribution ¾ Hypergeometric Probability Distributions 1 Expected Value and the Hypergeometric Distribution ¾ Deciding Between the Two Distributions ½ Key Questions What You Will Learn After completing this lesson, you will be able to analyze a given problem and decide whether the conditions of the problem represent a binomial distribution or a hypergeometric distribution create both graphical and algebraic representations of the binomial distribution and the hypergeometric distribution use the appropriate formula to solve probability and expected value problems for both binomial and hypergeometric distributions Copyright © 2009 The Ontario Educational Communications Authority. All rights reserved.

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Lesson 15 Mathematics of Data Management MDM4U-B 2 Binomial Probability Distributions Think of a situation in which you may have made a decision by tossing a coin. Maybe you were unsure what food you wanted to have with your hamburger, so you let the toss of a coin make the decision for you. If you tossed a “heads,” you ordered french fries but if you tossed a “tails,” you had a salad. Sometimes you don’t want just a single coin toss to make your decision, so you might prefer to use multiple tosses to help decide your fate. The situation described in the previous paragraph fits what is known as a binomial distribution . In an experiment involving a binomial distribution, the set of possible outcomes are accumulated through trials that are independent of one another and a single outcome can only be described as being a success or a failure . In other words, the “bi” in binomial indicates that there are only two possible outcomes. Referring back to the coin-tossing example, the outcome of each coin toss will not affect the outcome of the next one. Therefore, the coin tosses are independent of each other and there are only two possible outcomes when tossing a coin: heads or tails. However, it might be beneficial to think of the two possible outcomes as either “heads” and “not heads” or “tails” and “not tails.” This way, you are specifying what constitutes a success and what constitutes a failure. This idea will seem clearer if you imagine rolling a six- sided die. If success in a particular experiment was defined as rolling a 1, then failure would be NOT rolling a 1 or, in other words, rolling a 2, 3, 4, 5, or 6.
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