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

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

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

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 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)

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!*

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)

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? 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

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!) 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?

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

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