Theoretical Probability 10-6 Theoretical Probability Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

Warm Up 11/18/16 An experiment consists of spinning a spinner 8 times. The spinner lands on red 4 times, yellow 3 times, and green once. Find the experimental probability of each event. 1. The spinner lands on red. 2. The spinner does not land on green. 3. The spinner lands on yellow.

Objectives Determine the theoretical probability of an event. Convert between probabilities and odds.

Vocabulary equally likely theoretical probability fair complement odds

The theoretical probability of an event is the ratio of the number of ways the event can occur to the total number of equally likely outcomes.

When the outcomes in the sample space of an experiment have the same chance of occurring, the outcomes are said to be equally likely.

An experiment in which all outcomes are equally likely is said to be fair. You can usually assume that experiments involving coins and number cubes are fair.

Example An experiment consists of rolling a number cube. Find the theoretical probability of each outcome. rolling a 5 There is one 5 on a number cube.

Example An experiment consists of rolling a number cube. Find the theoretical probability of each outcome. rolling an odd number There 3 odd numbers on a cube. = 0.5 = 50%

Example: Finding Theoretical Probability rolling a number less than 3 There are 2 numbers less three.

The probability of an event can be written as P(event) The probability of an event can be written as P(event). P(heads) means “the probability that heads will be the outcome.” Reading Math

When you toss a coin, there are two possible outcomes, heads or tails When you toss a coin, there are two possible outcomes, heads or tails. The table below shows the theoretical probabilities and experimental results of tossing a coin 10 times.

The complement of an event is all the outcomes in the sample space that are not included in the event. The sum of the probabilities of an event and its complement is 1, or 100%, because the event will either happen or not happen. P(event) + P(complement of event) = 1

Example: Finding Probability by Using the Complement A box contains only red, black, and white blocks. The probability of choosing a red block is , the probability of choosing a black block is . What is the probability of choosing a white block? P(red) + P(black) + P(white) = 100% Either it will be a white block or not. 25% + 50% + P(white) = 100% 75% + P(white) = 100% –75% –75% Subtract 75% from both sides. P(white) = 25%

Example: Converting Between Odds and Probabilities The probability of rolling a 2 on a number cube is . What are the odds of rolling a 2 ? The probability of rolling a 2 is . There are 5 unfavorable outcomes and 1 favorable outcome, thus the odds are 1:5. Odds in favor are 1:5.

Lesson Quiz: Part I Find the theoretical probability of each outcome. 1. Randomly choosing B from the letters in ALGEBRA 2. Rolling a factor of 10 on a number cube 3. The probability that it will be sunny is 15%. What is the probability that it will not be sunny? 4. The probability of choosing a red marble out of a bag of marbles is . What are the odds in favor of choosing a red marble?

Lesson Quiz: Part II Find the theoretical probability of the outcome. 5. The odds against a spinner landing on blue are 7:5. Five sections of the spinner are red. What is the probability of the spinner landing on red?