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10-1. Probability. Course 3. Warm Up. Problem of the Day. Lesson Presentation. 3 6. 2 5. 3 5. 1 6. 2 5. 32 125. Warm Up Multiply. Write each fraction in simplest form. 1.  2. + Write each fraction as a decimal. 3. 4. 6 25. 2 3. 0.4. 0.256. Warm-Up.

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10-1

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

  2. 3 6 2 5 3 5 1 6 2 5 32 125 Warm Up Multiply. Write each fraction in simplest form. 1.  2. + Write each fraction as a decimal. 3. 4. 6 25 2 3 0.4 0.256

  3. Warm-Up • Reduce 12/15 to lowest terms • Change 2 ¾ to an improper fraction 3.

  4. 10-1 Probability Course 3 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

  5. 10-1 Probability Course 3 • 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.

  6. 10-1 Probability 1 1 3 4 2 4 Course 3 Never Happens about Always happens half the time happens 1 0 0 0.25 0.5 0.75 1 0% 25% 50% 75% 100%

  7. 10-1 Probability Course 3 The probabilities of all of the outcomes in a sample space mustadd up to 1 or 100%.

  8. 10-1 Probability Course 3 Give the probability for each outcome. 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%.

  9. 10-1 Probability Course 3 Give the probability for each outcome. 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%.

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

  11. 10-1 Probability 1 1 1 1 1 6 6 6 6 6 1 + + + + + = 1 6 Course 3 What is the probability of each outcome? Rolling a number cube.  Check The probabilities of all the outcomes must add to 1.

  12. 10-1 Probability 3 3 2 8 8 8 + + = 1 Course 3 Give the probability for each outcome.  Check The probabilities of all the outcomes must add to 1.

  13. 10-1 Probability Course 3 When finding the probability of one event OR the other, you simply add the probabilities together.

  14. 10-1 Probability Course 3 A quiz contains 5 true/false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. 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%

  15. 10-1 Probability Course 3 A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. 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%

  16. 10-1 Probability Course 3 A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. 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%

  17. 10-1 Probability Course 3 A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. 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%.

  18. Compound Probability

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

  20. 12 12 12 12 18 In each box, P(blue) = . · · = = 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) Multiply. P(blue, blue, blue) = 0.125

  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, then a green marble, and then a blue marble? In each box, P(green) = . 1 2 12 12 12 12 18 In each box, P(blue) = . · · = = Multiply. P(blue, green, blue) = 0.125

  22. 10-1 Probability Course 3 Insert Lesson Title Here 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) Lesson Quiz 0.351 0.874 0.794 0.004368

  23. 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?

  24. 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. 14 Course 3

  25. 10-1 Probability 1 1 1 4 4 • P(Roy) = P(Lee) =  0.4 = 0.1 Understand the Problem Course 3 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)

  26. 10-1 Probability Make a Plan 2 Course 3 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

  27. 10-1 Probability 4 Look Back Course 3 Check that the probabilities add to 1. 0.6 + 0.2 + 0.1 + 0.1 = 1 

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