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Chapter 6 Lesson 9 Probability and Predictions pgs. 310-314 What you’ll learn: Find the probability of simple events Use a sample to predict the actions of a larger group

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Vocabulary Outcomes (310): results of a probability problem Simple Event (310): one outcome or a collection of outcomes Probability (310): the chances of an event happening Sample Space (311): the set of all possible outcomes Theoretical Probability (311): what should occur Experimental Probability (311): what actually occurs when conducting a probability experiment

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Key Concept (310): Probability Words: The probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. Symbols: P(event) = number of favorable outcomes number of possible outcomes The probability of an event is always between 0 and 1, inclusive. The closer a probability is to 1, the more likely it is to occur.

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Example 1: Find Probability Ten cards are numbered 1 through 10, and one card is chosen at random. Determine the probability of drawing an even number. What we know: There are 10 cards We also know that 2,4,6,8,10 are even numbers. There are 10 possible outcomes: 1,2,3,4,5,6,7,8,9,10 P(even) = number of favorable outcomes number of possible outcomes P(even) = 5 = 1 10 2 So the probability of drawing an even number Is 1 or 50%. 2

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In Example 1, the set of all possible outcomes is called the sample space. What was the sample space for example 1? {1,2,3,4,5,6,7,8,9,10} notice the sample space is in brackets

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Example 2: Find Probability 123456 1(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) 2(2,1)(2,2)(2,3)(2,4)(2,5)(2,6) 3(3,1)(3,2)(3,3)(3,4)(3,5)(3,6) 4(4,1)(4,2)(4,3)(4,4)(4,5)(4,6) 5(5,1)(5,2)(5,3)(5,4)(5,5)(5,6) 6(6,1)(6,2)(6,3)(6,4)(6,5)(6,6) Pg. 311 These are all the possible outcomes of rolling 2 dice, each with the numbers 1-6. This is the sample space.

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Refer to the previous chart P(event) = Number of favorable outcomes Number of possible outcomes Suppose two dice are rolled. Find the probability of rolling an odd sum. Take a look at the sample space, add all the sums Ex. (1,2) = 3 and count how many are odd There are 18 outcomes in which the sum is odd. So, P(odd)= 18 = 1 = 50% 36 2 This means there is a 50% chance of rolling an odd sum.

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The Probabilities in Example 1 & 2 are Theoretical Probability---what should happen Example 3: Find Experimental Probability (what actually occurs) OutcomeTallyFrequency HeadsIIII IIII IIII 14 TailsIIII IIII I 11 This table shows the results of an experiment in which a coin was Tossed. Find the experimental probability of tossing a coin and getting tails for this experiment. Number of times tails occur = 11 = 11 Number of possible outcomes 14+11 25 The experimental Probability of getting Tails in this case is 11 25 or 44%

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Example 4: Make a Prediction Mary took a sample from a package of jellybeans and found that 30% of the beans were red. Suppose there are 250 jellybeans in the package. How many can she expect to be red? The total number of jellybeans is 250, so 250 is the base. The percent is 30%. You can choose to use the percent proportion or the percent equation. Let’s look at both ways.

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Percent Proportion Way: Mary took a sample from a package of jellybeans and found that 30% of the beans were red. Suppose there are 250 jellybeans in the package. How many can she expect to be red? The total number of jellybeans is 250, so 250 is the base. The percent is 30%. n = 30 250 100 100 n = 250 30 100n = 7500 100 n = 75 So, Mary could Expect 75 of the Jellybeans to be red.

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Percent Equation Way: Mary took a sample from a package of jellybeans and found that 30% of the beans were red. Suppose there are 250 jellybeans in the package. How many can she expect to be red? The total number of jellybeans is 250, so 250 is the base. The percent is 30%. Part = Percent Base n =.30(250) n = 75 So, as you can see that by using Either formula, Mary could Expect 75 of the jellybeans to be Red.

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Your Turn! There are 4 blue marbles, 6 red marbles, 3 green marbles, and 2 yellow marbles in a bag. Suppose you select one marble at random. Find the probability of each out come. Express each probability as a fractions and as a percent. Round to the nearest percent. A. P(green) B. P(red or yellow) P(green) = 3 = 1 = 20% 15 5 P(red or yellow) = 8 ; 53% 15

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Your Turn Again! Suppose two number cubes are rolled. What is the probability of rolling a sum greater than 8? Refer to the sample space on pg. 311. 10 = 5 ; about 28% 36 18 A sample from a package of assorted cookies revealed That 20% of the cookies were sugar cookies. Suppose there are 45 cookies in the package. How many can be expected to be sugar cookies? n = 20n =.20(45) 45 100OR n = 9 n 100 = 45 20Using either formula, you could 100n = 900 n = 9 expect 9 cookies to be sugar.

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Quiz over 6-8 & 6-9 tomorrow! We will be reviewing on Thursday and testing on Friday over Chapter 6.

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