1. 10-1 Probability Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

3. Warm Up Multiply. Write each fraction in simplest form. 1. 2. + Write each fraction as a decimal. 3.4. 6 25 2323 0.4 3636 2525 3535 1616 2525 32 125 0.256

4. Warm-Up 1.Reduce 12/15 to lowest terms 2.Change 2 ¾ to an improper fraction 3. FractionDecimalPercent 8/25 5.25 3%

5. Course 3 10-1 Probability Each observation of an experiment is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment. ExperimentSample Space  flipping a coin----  rolling a number cube --  guessing the number of marbles in a jar---  heads, tails  1, 2, 3, 4, 5, 6  whole numbers

6. Course 3 10-1 Probability The probability of an event occurring can written as a decimal, fraction, or percent. A probability of 0 means the event is impossible, or can never happen. A probability of 1 or 100% means the event is certain, or has to happen.

7. Course 3 10-1 Probability 0 0.25 0.5 0.75 1 NeverHappens about Always happenshalf the timehappens 1 4 1 2 3 4 0 1 0% 25% 50% 75% 100%

8. Course 3 10-1 Probability The probabilities of all of the outcomes in a sample space must add up to 1 or 100%.

9. Give the probability for each outcome. Course 3 10-1 Probability The basketball team has a 70% chance of winning. The probability of winning is P(win) = 70% = 0.7. The probabilities must add to 1 or 100%, so the probability of not winning, P(lose) = 1 – 0.7 = 0.3, or 30%.

10. Give the probability for each outcome. Course 3 10-1 Probability The polo team has a 60% chance of winning. The probability of winning is P(win) = 60% = 0.6. The probabilities must add to 1 or 100%, so the probability of not winning, P(lose) = 1 – 0.6 = 0.4 or 40%.

11. Course 3 10-1 Probability Probability, when written as a fraction: Outcome you are looking for All possible outcomes

12. What is the probability of each outcome? Course 3 10-1 Probability Rolling a number cube. Outcome 123456 Probability Check The probabilities of all the outcomes must add to 1. 1 6 1 6 1 6 ++ = 1 1 6 + 1 6 + 1 6 +

13. Give the probability for each outcome. Course 3 10-1 Probability 3 8 3 8 2 8 ++ = 1 Check The probabilities of all the outcomes must add to 1.

14. Course 3 10-1 Probability When finding the probability of one event OR the other, you simply add the probabilities together.

15. A quiz contains 5 true/false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. Course 3 10-1 Probability What is the probability of guessing 1 or more correct? The event “one or more correct” consists of the outcomes 1, 2, 3, 4, or 5. P(1 or more correct) = 0.156 + 0.313 + 0.313 + 0.156 + 0.031 = 0.969 or 96.9%

16. Course 3 10-1 Probability What is the probability of guessing fewer than 3 correct? The event “fewer than 3” consists of the outcomes 0, 1, or 2. P(fewer than 3) = 0.031 + 0.156 + 0.313 = 0.5 or 50% A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

17. Course 3 10-1 Probability What is the probability of guessing fewer than 2 correct? The event “fewer than 2 correct” consists of the outcomes 0 or 1. P(fewer than 2 correct) = 0.031 + 0.156 = 0.187 or 18.7% A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

18. Course 3 10-1 Probability What is the probability of guessing 2 or more correct? The event “two or more correct” consists of the outcomes 2, 3, 4, or 5. P(2 or more) = 0.313 + 0.313 + 0.156 + 0.031 =.813 or 81.3%.

20. Vocabulary A compound event is made up of one or more separate events. P(event, event) is the same as P(event and event) And (in probability) means to multiply.

21. Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box. What is the probability of choosing a blue marble from each box? P (blue, blue, blue) P(blue, blue, blue) = In each box, P(blue) =. 1212 1212 · 1212 · 1212 = 1818 = 0.125 Multiply.

22. Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box. What is the probability of choosing a blue marble, then a green marble, and then a blue marble? P(blue, green, blue) = 1212 · 1212 · 1212 = 1818 = 0.125 Multiply. In each box, P(blue) =. 1212 In each box, P(green) =. 1212

23. Lesson Quiz Use the table to find the probability of each event. 1. P(1 or 2) 2. P(not 3) 3. P(2, 3, or 4) 4. P(1 and 5) 0.874 0.351 Insert Lesson Title Here 0.794 Course 3 10-1 Probability 0.004368

24. Closing What do you do when you see the word AND in probability? What do you do when you see the word OR in probability? What do you do when you see the word NOT in probability?

25. Course 3 10-1 Probability Six students are in a race. Ken’s probability of winning is 0.2. Lee is twice as likely to win as Ken. Roy is as likely to win as Lee. Tracy, James, and Kadeem all have the same chance of winning. Create a table of probabilities for the sample space. 1414

26. Course 3 10-1 Probability 1 Understand the Problem The answer will be a table of probabilities. Each probability will be a number from 0 to 1. The probabilities of all outcomes add to 1. List the important information: P(Ken) = 0.2 P(Lee) = 2  P(Ken) = 2  0.2 = 0.4 P(Tracy) = P(James) = P(Kadeem) P(Roy) =  P(Lee) =  0.4 = 0.1 1 4 1 4

27. Course 3 10-1 Probability 2 Make a Plan You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Tracy, James, and Kadeem. P(Ken) + P(Lee) + P(Roy) + P(Tracy) + P(James) + P(Kadeem) = 1 0.2 + 0.4 + 0.1 + p + p + p = 1 0.7 + 3p = 1

28. Course 3 10-1 Probability Look Back4 Check that the probabilities add to 1. 0.6 + 0.2 + 0.1 + 0.1 = 1