Bell Quiz

Objectives Calculate probabilities of simple events. Express probabilities as fractions, decimals, or percents.

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.)

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.

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

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

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%.

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

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)

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?

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?

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?

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?

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