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Probability is probably more useful in real life than most math courses students take and the SAT's are including more and more probability problems. It is a growing part of the common core. Still, it is frequently the forgotten child of mathematics. In many high schools, it is not formally taught.
Probability is part of the AP Statistics curriculum but just as a background for hypothesis testing. Combinations and permutations are barely mentioned. In many schools, probability is sort of thrown in at the end of algebra 2 and students struggle with it because many teachers don't understand it, as they had no formal course in it. Examples and exercises in a chapter or so are barely sufficient in an area where students need a lot of repetition to become proficient.
This unit is a full course in probability. It will take about a month to teach. It starts with basic probability definitions and simple probability problems. It moves into counting techniques, which is necessary to determine how many ways an experiment can occur. Teaching permutations and combinations allows us to then count the outcomes that are favorable to us. Once that occurs, finding probability is simple because students will be experts at finding both the numerator and denominators.
A great deal of time is spent on conditional probability because there are so many real-life examples of it. From there, we then use probability to find expected value.
We conclude with in-depth studies of 3 distributions: binomial, geometric, and Poisson (which is not usually taught). We also show how using basic geometry can help us solve certain types of continuous distribution probability questions. We conclude with a section of how probability can help us in making decisions.
This probability manual is in the same format as our popular Calculus and Precalculus courses. There are classwork problems that are meant to be solved as part of a classroom setting and then homework problems that students are expected to solve on their own. As usual, the student version is FREE.
The unit has the usual types of problems, coin tossing, card playing, and dice throwing marbles in a bag. But there are new and relevant examples and exercises such as dealing with telemarketers, Lyme disease, heart arrhythmias, airport security, and peanut allergies to name just a few. Since it is part of a precalculus unit, a few of the problems are more challenging than the typical "how many ways can 5 people line up?". Teachers will have no problem teaching from it because of the number of worked out exercises.
Below are the free links to the student versions.
. The Birthday Problem . The Boy/Girl Paradox
. The Monty Hall Problem . Simpson's Rule
. The Elevator Problem . The Hat-Check Problem
. The Secretary Problem . The Dartboard Paradox
Also, you get 3 exams and solutions. These are not given as part of our free version so that students do not have access to them.
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