2. 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
3. Practice Problems ex) 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 Principle There are 2 ways to count the number of possible outcomes. 1) make a tree diagram 2) use the Fundamental Counting Principle
5. Tree Diagrams Ex) 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 Events EQ: How do you calculate compound events?
8. 9-7 Independent & Dependent Events compound event: an event made up of two or more simple events independent events: one event has no effect on the probability of the second event dependent 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 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
10. Calculating Compound Probabilities 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) * When calculating the compound probabilities, just multiply the probability of each event together. Don’t forget to reduce!*
11. More Compound Probability There 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)
13. 9-2 & 9-4 Experimental & Theoretical Probability EQ: 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. 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?
16. ***When conducting experiments, the experimental probability will get closer to the theoretical probability as you do the experiment more often!***
