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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 16. 12. 1. 1. 4. 1. 20. 36. 3. 5. 5. 8. 39. 195. Warm Up Write each fraction in simplest form. 1. 2. 3. 4. 8. 64. California Standards. Review of Grade 6

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 16 12 1 1 4 1 20 36 3 5 5 8 39 195 Warm Up Write each fraction in simplest form. 1. 2. 3. 4. 8 64

  3. California Standards Review of Grade 6 SDAP3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1 – P is the probability of an event not occurring.

  4. Vocabulary experiment trial outcome sample space event probability

  5. An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment. Experiment Sample Space flipping a coin heads, tails rolling a number cube 1, 2, 3, 4, 5, 6

  6. An event is any set of one or more outcomes. The probability of an event is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen. You can write probability as a fraction, a decimal, or a percent. • A probability of 0 means the event is impossible, or can never happen. • A probability of 1 means the event is certain, or will always happen. • The probabilities of all the outcomes in the sample space add up to 1.

  7. 1 1 3 4 2 4 Never Happens about Always happens half the time happens 1 0 0 0.25 0.5 0.75 1 0% 25% 50% 75% 100%

  8. Additional Example 1A: Finding Probabilities of Outcomes in a Sample Space Give the probability for each outcome. The basketball team has a 70% chance of winning. P(win) = 70% = 0.7. P(lose) = 1 – 0.7 = 0.3, or 30%

  9. 3 8 Three of the eight sections of the spinner are labeled 1, so is a reasonable estimate. P(1) = Additional Example 1B: Finding Probabilities of Outcomes in a Sample Space Give the probability for each outcome. 3 8

  10. P(2) = P(3) = Two of the eight sections of the spinner are labeled 3, so is a reasonable estimate. Three of the eight sections of the spinner are labeled 2, so is a reasonable estimate. 3 2 3 3 2 3 8 2 8 8 8 8 8 8 + + = 1 Additional Example 1B Continued Check The probabilities of all the outcomes must add to 1. 

  11. Check It Out! Example 1A Give the probability for each outcome. The polo team has a 50% chance of winning. P(win) = 50% = 0.5. P(lose) = 1 – 0.5 = 0.5, or 50%.

  12. 3 8 Three of the eight sections of the spinner are teal, so is a reasonable estimate. P(teal) = Check It Out! Example 1B Give the probability for each outcome. 3 8

  13. P(red) = P(orange) = Three of the eight sections of the spinner are red, so is a reasonable estimate. 3 3 3 2 2 3 8 8 8 8 8 8 Two of the eight sections of the spinner are orange, so is a reasonable estimate. 2 8 + + = 1 Check It Out! Example 1B Continued Check The probabilities of all the outcomes must add to 1. 

  14. To find the probability of an event, add the probabilities of all the outcomes included in the event.

  15. Additional Example 2A: Finding Probabilities of Events 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 3 or more correct? The event “three or more correct” consists of the outcomes 3, 4, and 5. P(3 or more correct) = 0.313 + 0.156 + 0.031 = 0.5, or 50%.

  16. Additional Example 2B: Finding Probabilities of Events 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 fewer than 2 correct? The event “fewer than 2 correct” consists of the outcomes 0 and 1. P(fewer than 2 correct) = 0.031 + 0.156 = 0.187, or 18.7%.

  17. Check It Out! Example 2A 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 2 or more correct? The event “two or more correct” consists of the outcomes 2, 3, 4, and 5. P(2 or more) = 0.313 + 0.313 + 0.156 + 0.031 = 0.813, or 81.3%.

  18. Check It Out! Example 2B 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 fewer than 3 correct? The event “fewer than 3” consists of the outcomes 0, 1, and 2. P(fewer than 3) = 0.031 + 0.156 + 0.313 = 0.5, or 50%.

  19. Lesson Quiz Use the table to find the probability of each event. 1. 1 or 2 occurring 2. 3 not occurring 3. 2, 3, or 4 occurring 0.351 0.874 0.794

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