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## 10-5, 10-6, 10-7 Probability

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**10-5, 10-6, 10-7Probability**EQ: How is the probability of multiple events calculated?**Probability**Probability: the chance that an event will happen - a probability of 1 means the event is certain - a probability of 0 means the event is impossible Outcome: a result of an experiment (ex: a bag has 4 marbles = 4 outcomes) Sample Space: a list of all the possible outcomes of an experiment**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**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)**Independent & Dependent Events**EQ: How do you calculate compound events?**Vocabulary**compound event: an event made up of two or more simple events**Indepedent Events**independent events: one event has no effect on the probability of the second event- multiply the probabilities together Examples1) 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)**Calculating Independent Events*** When calculating the compound probabilities, just multiply the probability of each event together. Don’t forget to reduce!* Find the compound probabilities1. 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)**Dependent Events**dependent events: one event does have an effect on the probability of the second event (multiply the probabilities together) Examples1) 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 bydrawing 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**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)**Independent or Dependent?**• Rolling a 2 on a dice then spinning yellow on a spinner • Picking a orange Skittle out of a bag and eating it, then picking a red Skittle • Picking a Jack out of a deck of cards then selecting a ten out of the deck**Experimental & Theoretical Probability**EQ: What is the difference between theoretical & experimental probability?**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?**Theoretical**Theoretical probability is used to estimate probabilities when the outcomes are equally likely (what should happen!) 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? 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?*****When conducting experiments, the**experimental probability will get closer to the theoretical probability as you do the experiment more often!***