STA 301 - Ch 02 - pp 27-32

STA 301 - Ch 02 - pp 27-32 - Chapter 2 Probability COUNTING...

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27 COUNTING RULES As we begin our study of probability, we will often need to know the number of elements in our sample space. The following counting rules can help determine sample space size without needing to list all elements. Multiplication rule If an operation can be performed in 1 n ways, and for each of these ways, a second operation can be performed in 2 n ways, then the two operations together can be performed in 2 1 n n ways. Example: How many different outcomes are there when rolling 2 dice? Generalized multiplication rule If an operation can be performed in 1 n ways, and for each of these a second operation can be performed in 2 n ways, and for each of these a third operation can be performed 3 n ways, … , and for each of these a k th operation can be performed k n ways, then together the k operations can be performed k n n n L 2 1 ways. Example: A pizzeria offers the following choices for single-topping pizzas. Sizes: 10”, 14”, 18”
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STA 301 - Ch 02 - pp 27-32 - Chapter 2 Probability COUNTING...

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