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Bell Quiz

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**Objectives Calculate probabilities of simple events.**

Express probabilities as fractions, decimals, or percents.

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Sample Space A sample space is the set of all possible outcomes of an event. For example, a toss of a fair coin has two equally like outcomes. Heads Tails (This is the sample space.)

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**Simple Event A simple event is an event having only one outcome.**

For example, rolling a 5 on a number cube is a simple event.

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**Example 1 Identifying Sample Space**

A number cube labeled 1 – 6 is rolled. List the outcomes for each event. A number less than or equal to 3 An odd number A number greater than 4

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Lesson Practice A number cube labeled 1 – 6 is rolled. List the outcomes for each event. A number less than or equal to 4 An even number A number greater than 2

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**Theoretical Probability**

The theoretical probability of an out come is found by analyzing a situation in which all outcomes are equally likely. Then finding the ratio of favorable outcomes to all possible outcomes. For example, the probability of tossing a coin and it landing on heads is ½ or 0.5 or 50%.

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**Theoretical Probability**

Theoretical Probability can be determined using the following formula: number of favorable outcomes P(event) = total number of outcomes

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Complement of an Event A complement of an event is a set of all outcomes of an experiment that are not in a given event. For example, if heads is the desired event when tossing a coin, tails is the complement of the event. The sum of an event and its complement equals 1 P(event) + P(not event) = 1 P(not event) = 1 – P(event)

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**Example 2 Calculating Theoretical Probability**

There are 4 green, 3 blue, and 3 red marbles in a bag. Give each answer as a decimal and as a percent. What is the probability of randomly choosing a red marble? What is the probability of randomly choosing a marble that is not green?

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**Lesson Practice There are 4 green, 3 blue, and 3 red marbles in a bag.**

What is the probability of randomly choosing a blue marble? What is the probability of randomly choosing a marble that is not red?

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**Example 3 Calculating Chance**

In a bucket there are 10 balls numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number greater than 4? Is there a greater chance of drawing a number greater than 4 or drawing a 1?

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Lesson Practice Suppose there are 8 balls in a bucket numbered as follows: 1, 2, 3, 5, 5, 6, 7, and 7. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number less than 6? Do you have a greater chance of drawing a 7 or a 6?

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Example 4 Application A 52-card deck has 4 kings. What is the probability of randomly drawing a king out of the deck?

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