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9.3 Counting Principles

9.3 Counting Principles. Lesson Obj : IWBAT to determine if events are mutually exclusive, inclusive, independent or dependent. Guiding Question: What ways do we have to count outcomes for events?.

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9.3 Counting Principles

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  1. 9.3 Counting Principles Lesson Obj: IWBAT to determine if events are mutually exclusive, inclusive, independent or dependent.

  2. Guiding Question: What ways do we have to count outcomes for events? • Fundamental Counting Principle: If there are m ways an event can occur and n ways another event can occur, then the total ways both can occur is m x n. • If you have 9 shirts, 8 pairs of pants, and 6 pairs of shoes, how many outfits can you have? 6*8*9= 432 possible outfits.

  3. Guiding Question: What ways do we have to count outcomes for events? Independent events – Events that occur with no effect on each other. Dependent events – the 2nd event effects the first. Ex. Draw a card, keep it, and draw another card. - Probability of A times the probability of B given A has occurred. Ex. Draw a card and roll a die Where A and B are independent events.

  4. Guiding Question: What ways do we have to count outcomes for events? • Consider rolling 2 dice… Is rolling each dice independent? Why? What if you were taking the sum of the 2 dice, still independent?

  5. Guiding Question: What ways do we have to count outcomes for events? Is playing blackjack dependent or independent? What are the various ways to get blackjack? There are 2 ways to get blackjack (Ace, facecard) or (facecard, Ace) This type of situation is said to be mutually exclusive. (One event occurring prevents the other from occurring)

  6. Guiding Question: What ways do we have to count outcomes for events? Mutually Exclusive: 2 events that cannot happen at the same time. Overlapping (Inclusive events) – 2 events that can occur at same time.

  7. Guiding Question: What ways do we have to count outcomes for events? • Assignment: Q1-Q5, Q7-10, 1-15 odd, 16

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