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10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?

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Probability Probability: the chance that an event will happen Outcome: a result of an experiment (ex: a bag has 4 marbles = 4 outcomes) - a probability of 1 means the event is certain - a probability of 0 means the event is impossible Sample Space: a list of all the possible outcomes of an experiment

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There are 2 ways to count the number of possible outcomes. 1) make a tree diagram 2) use the Counting Principle Ex) Three shirts, 4 pairs of pants, and 2 pairs of shoes. How many outfits are possible? Try) 3 dice are rolled

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Jigsaw You will work with a group to become an expert on a certain topic. Then you will work with another group and teach them your topic Everyone will be a student and a teacher today A = independent events (10-7, p. 727) B = dependent events (10-7, p. 729) C = theoretical probability (10-6, p. 720) D = experimental probability (10-5, p. 713)

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Independent & Dependent Events EQ: How do you calculate compound events?

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Vocabulary compound event: an event made up of two or more simple events

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Indepedent Events independent events: one event has no effect on the probability of the second event- multiply the probabilities together Examples 1) Selecting a marble from a bag then picking a card from a deck of cards 2) Picking a popsicle stick out of Mrs. Price’s cup of fun, returning it, then picking another popsicle stick There are 5 yellow Skittles, 3 purple Skittles, 1 red Skittle, and 1 green Skittle. Once a Skittle is picked, it is placed back in the bag. 1. Find the P(yellow) then P(purple) 2. Find the P(red) then P(yellow)

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Calculating Independent Events Find the compound probabilities 1. Find the probability of flipping a coin and getting tails and then rolling a 4 on a number cube. P(tails) then P(4) 2. P(red card) then P(odd on a number cube) 3. P(6) then P(6) * When calculating the compound probabilities, just multiply the probability of each event together. Don’t forget to reduce!*

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Dependent Events Examples 1) Selecting a red Skittle and eating it and then picking out another red Skittle 2) Drawing an Ace out of a deck of cards followed by drawing a red ten There are 8 yellow Skittles, 2 purple Skittles, 2 red Skittle, and 3 green Skittle. Once a Skittle is picked, it is not returned to the bag. 1. Find the P(yellow) then P(green) 2. Find the P(red) then P(purple) dependent events: one event does have an effect on the probability of the second event (multiply the probabilities together)

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Dependent Events There are 4 blue socks, 2 red socks, 2 brown socks, and 4 white socks in a drawer. 1. P(blue) then P(red) (not replaced) 2. P(white) then P(white) (not replaced) 3. P(blue) then P(blue) then P(blue) (not replaced)

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Independent or Dependent? 1)Rolling a 2 on a dice then spinning yellow on a spinner 2)Picking a orange Skittle out of a bag and eating it, then picking a red Skittle 3)Picking a Jack out of a deck of cards then selecting a ten out of the deck

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Experimental & Theoretical Probability EQ: What is the difference between theoretical & experimental probability?

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In experimental probability, the likelihood of an event is estimated by repeating an experiment many times and observing what happens (What actually happens!) Example: Jane pulled a card out of a deck of 52 cards. Jane would replace the card after each draw. After 100 trials, she had pulled a red card 58 times and a black card 42 times. What is the experimental probability of pulling out 1) a red card? 2) a black card?

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Theoretical Theoretical probability is used to estimate probabilities when the outcomes are equally likely (what should happen!) Try… If the numbers 0-9 are written on slips of paper and placed in a hat, what is the theoretical probability of selecting the 4? When flipping a coin, what is the theoretical probability of it landing on tails? Example: There are 20 jellybeans in a jar (5 blue, 5 red, 5 orange, 5 yellow). If I pull 4 jellybeans out, what should happen?

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***When conducting experiments, the experimental probability will get closer to the theoretical probability as you do the experiment more often!***

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