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9-4 Theoretical Probability Theoretical probability is used to find the probability of an event when all the outcomes are equally likely. Equally likely outcomes have the same probability. If each possible outcome of an experiment is equally likely, then the experiment is said to be fair. Experiments involving number cubes and coins are usually assumed to be fair.

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9-4 Theoretical Probability Andy has 20 marbles in a bag. Of these, 9 are clear and 11 are blue. Find the probability of drawing a clear marble from the bag. Write your answer as a fraction, as a decimal, and as a percent. P = number of ways the event can occur total number of equally likely outcomes P(clear) = number of clear marbles total number of marbles

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9-4 Theoretical Probability Find the probability of drawing a blue marble from the bag. P = number of ways the event can occur total number of equally likely outcomes

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9-4 Theoretical Probability drawing a ball numbered 4 or lower Check It Out: Example 1A Dalek is drawing numbered balls from a bin. There are 20 balls numbered 1 through 20. Find the probability of each event. Write your answer as fraction, a decimal, and a percent.

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9-4 Theoretical Probability Dalek is drawing numbered balls from a bin. There are 20 balls numbered 1 through 20. Find the probability of each event. Write your answer as fraction, a decimal, and a percent. drawing an odd-numbered ball

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9-4 Theoretical Probability There are 13 boys and 10 girls on the track team. The name of each of the team members is written on an index card. A card is drawn at random to choose a student to run a sprint and the card is replaced in the stack. Find the theoretical probability of drawing a boy’s name.

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9-4 Theoretical Probability The sum of the probabilities of an event and its complement is 1. Remember!

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9-4 Theoretical Probability Find the theoretical probability of drawing a girl’s name. There are 13 boys and 10 girls on the track team. The name of each of the team members is written on an index card. A card is drawn at random to choose a student to run a sprint and the card is replaced in the stack.

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9-4 Theoretical Probability There are 15 boys and 12 girls in Sharon’s math class. Each of their names is written on a slip of paper and put in a hat. Find the theoretical probability of drawing a boy’s name.

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9-4 Theoretical Probability There are 15 boys and 12 girls in Sharon’s math class. Each of their names is written on a slip of paper and put in a hat. Find the theoretical probability of drawing a girl’s name.

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9-4 Theoretical Probability Find the probabilities. Write your answer as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. You have 11 cards, each with one of the letters from the word mathematics. 1. Find the probability of drawing an m from the pile of shuffled cards. 2. Find the probability of drawing a vowel. 3. Find the probability of drawing a consonant.

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9-4 Theoretical Probability 1. A number cube is rolled. Identify the probability of getting a number less than 4 as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent.

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9-4 Theoretical Probability 2. There are 40 balls in a bag. Of these 8 are white, 7 are blue, 12 are green, and 13 are yellow. Identify the probability of drawing a white ball as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent.

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