There are two ways to count the number of possible outcomes of an experiment: 1) Using a tree diagram to list out all the combinations 2) Using the Fundamental Counting Principle, which involves multiplying the number of choices for each event together. To calculate the probability of compound events (events made up of two or more simple events), you first determine if the events are independent or dependent. For independent events, the probability of one event does not affect the other event. You calculate the probability by multiplying the individual probabilities together.

1. ProbabilityEQ: What are the two ways to count the number of outcomes?

2. ProbabilityProbability: the chance that an event will happen- a probability of 1 means the event is certain- a probability of 0 means the event is impossibleOutcome: 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

3. Practice Problemsex) What is the probability of selecting a red card out of a deck of cards?Try) a) P(king) = b) P(club) =Try) On a number cube, what is the… a) P(odd) = b) P(less than 7) = c) P (2 or 3) = d) P(prime) =

4. 9-5 The Counting PrincipleThere are 2 ways to count the number of possible outcomes.1) make a tree diagram2) use the Fundamental Counting Principle

5. Tree DiagramsEx) For lunch you have the choice of wheat or white bread. For the filling you could have turkey or veggies. For cheese you could have Swiss, American, or soy cheese. How many different types of sandwiches are possible?

6. The Easier Method…Fundamental Counting Principle: multiplying the number of choices for each event together Ex) Three shirts, 4 pairs of pants, and 2 pairs of shoes. How many outfits are possible?Try) 5 flavors of ice cream. Cone or no cone. Sprinkles, hot fudge, cherry, oreos. How many types of sundaes?Try) 6 questions on a true/false quiz. How many possible outcomes?Try) A coin is tossed, a die is rolled, another coin is tossed.Try) 3 dice are rolled

7. 9-7 Independent & Dependent EventsEQ: How do you calculate compound events?

8. 9-7 Independent & Dependent Eventscompound event: an event made up of two or more simple eventsindependent events: one event has no effect on the probability of the second eventdependent events: one event does have an effect on the probability of the second event

9. Independent or Dependent?Rolling a 2 on a dice then spinning yellow on a spinnerPicking 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

10. Calculating Compound ProbabilitiesFind 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)* When calculating the compound probabilities, just multiply the probability of each event together. Don’t forget to reduce!*

11. More Compound ProbabilityThere are 4 blue socks, 2 red socks, 2 brown socks, and 4 white socks in a drawer.4. P(blue) then P(red) (not replaced)5. P(white) then P(white) (not replaced)6. P(brown) then P(brown) (replaced)7. P(blue) then P(blue) then P(blue) (not replaced)8. P(red) then P(green) (replaced)

12. HOMEWORK!Workbookp. 77 All

13. 9-2 & 9-4 Experimental & Theoretical ProbabilityEQ: What is the difference between theoretical & experimental probability?

14. 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?

15. TheoreticalTheoretical 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?

16. ***When conducting experiments, theexperimental probability will get closer to thetheoretical probability as you do theexperiment more often!***