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Pre-Algebra 9-1 Probability 9-1 Probability Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Pre-Algebra 9-1 Probability Warm Up Write each fraction in simplest form Pre-Algebra 9-1 Probability

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Pre-Algebra 9-1 Probability Problem of the Day A careless reader mixed up some encyclopedia volumes on a library shelf. The Q volume is to the right of the X volume, and the C is between the X and D volumes. The Q is to the left of the G. X is to the right of C. From right to left, in what order are the volumes? D, C, X, Q, G

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Pre-Algebra 9-1 Probability Learn to find the probability of an event by using the definition of probability.

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Pre-Algebra 9-1 Probability Vocabulary experiment trial outcome sample space event probability impossible certain

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Pre-Algebra 9-1 Probability 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. ExperimentSample Space flipping a coin heads, tails rolling a number cube 1, 2, 3, 4, 5, 6 guessing the number of whole numbers jelly beans in a jar

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Pre-Algebra 9-1 Probability An event is any set of one or more outcomes. The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen. A probability of 0 means the event is impossible, or can never happen. A probability of 1 means the event is certain, or has to happen. The probabilities of all the outcomes in the sample space add up to 1.

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Pre-Algebra 9-1 Probability % 25% 50% 75% 100% NeverHappens about Always happenshalf the timehappens

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Pre-Algebra 9-1 Probability Give the probability for each outcome. Additional Example 1A: Finding Probabilities of Outcomes in a Sample Space A. 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, so the probability of not winning is P(lose) = 1 – 0.7 = 0.3, or 30%.

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

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Pre-Algebra 9-1 Probability Additional Example 1B Continued Three of the eight sections of the spinner are labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) =. 3 8 Two of the eight sections of the spinner are labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = = Check The probabilities of all the outcomes must add to = 1

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Pre-Algebra 9-1 Probability Give the probability for each outcome. Try This: Example 1A A. The polo team has a 50% chance of winning. The probability of winning is P(win) = 50% = 0.5. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.5 = 0.5, or 50%.

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Pre-Algebra 9-1 Probability Give the probability for each outcome. Try This: Example 1B B. Rolling a number cube. One of the six sides of a cube is labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P(1) =. 1 6 Outcome Probability One of the six sides of a cube is labeled 2, so a reasonable estimate of the probability that the spinner will land on 1 is P(2) =. 1 6

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Pre-Algebra 9-1 Probability Try This: Example 1B Continued One of the six sides of a cube is labeled 3, so a reasonable estimate of the probability that the spinner will land on 1 is P(3) =. 1 6 One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 1 is P(4) =. 1 6 One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 1 is P(5) =. 1 6

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Pre-Algebra 9-1 Probability Try This: Example 1B Continued One of the six sides of a cube is labeled 6, so a reasonable estimate of the probability that the spinner will land on 1 is P(6) =. 1 6 Check The probabilities of all the outcomes must add to =

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Pre-Algebra 9-1 Probability To find the probability of an event, add the probabilities of all the outcomes included in the event.

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Pre-Algebra 9-1 Probability A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. Additional Example 2A: Finding Probabilities of Events A. What is the probability of not guessing 3 or more correct? The event not three or more correct consists of the outcomes 0, 1, and 2. P(not 3 or more) = = 0.5, or 50%.

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Pre-Algebra 9-1 Probability A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. B. What is the probability of guessing between 2 and 5? The event between 2 and 5 consists of the outcomes 3 and 4. P(between 2 and 5) = = 0.469, or 46.9% Additional Example 2B: Finding Probabilities of Events

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Pre-Algebra 9-1 Probability A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. C. What is the probability of guessing an even number of questions correctly (not counting zero)? The event even number correct consists of the outcomes 2 and 4. P(even number correct) = = 0.469, or 46.9% Additional Example 2C: Finding Probabilities of Events

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Pre-Algebra 9-1 Probability A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. Try This: Example 2A A. 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) = = 0.5, or 50%.

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Pre-Algebra 9-1 Probability A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. B. 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) = = 0.5, or 50% Try This: Example 2B

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Pre-Algebra 9-1 Probability A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. C. What is the probability of passing the quiz (getting 4 or 5 correct) by guessing? The event passing the quiz consists of the outcomes 4 and 5. P(passing the quiz) = = 0.187, or 18.7% Try This: Example 2C

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Pre-Algebra 9-1 Probability Additional Example 3: Problem Solving Application Six students are in a race. Kens 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

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Pre-Algebra 9-1 Probability Additional Example 3 Continued 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) = = 0.4 P(Tracy) = P(James) = P(Kadeem) P(Roy) = P(Lee) = 0.4 =

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Pre-Algebra 9-1 Probability Additional Example 3 Continued 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) = p + p + p = p = 1

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Pre-Algebra 9-1 Probability Solve p = 1 –0.7 –0.7 Subtract 0.7 from both sides. 3p = 0.3 3p3p = Divide both sides by 3. Additional Example 3 Continued p = 0.1

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Pre-Algebra 9-1 Probability Look Back4 Check that the probabilities add to = 1 Additional Example 3 Continued

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Pre-Algebra 9-1 Probability Four students are in the Spelling Bee. Freds probability of winning is 0.6. Willas chances are one-third of Freds. Bettys and Barries chances are the same. Create a table of probabilities for the sample space. Try This: Example 3

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Pre-Algebra 9-1 Probability Try This: Example 3 Continued 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(Fred) = 0.6 P(Betty) = P(Barrie) P(Willa) = P(Fred) = 0.6 =

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Pre-Algebra 9-1 Probability Try This: Example 3 Continued 2 Make a Plan You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Betty and Barrie. P(Fred) + P(Willa) + P(Betty) + P(Barrie) = p + p = p = 1

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Pre-Algebra 9-1 Probability Solve p = 1 –0.8 –0.8Subtract 0.8 from both sides. 2p = 0.2 Try This: Example 3 Continued OutcomeFredWillaBettyBarrie Probability p = 0.1

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Pre-Algebra 9-1 Probability Look Back4 Check that the probabilities add to = 1 Try This: Example 3 Continued

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Pre-Algebra 9-1 Probability Lesson Quiz Use the table to find the probability of each event or 2 occurring 2. 3 not occurring 3. 2, 3, or 4 occurring

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