Probability and Odds pg Vocabulary

Outcomes The possible results of an experiment. Ex. When you roll a number cube, there are 6 possible outcomes.

Event An event is an outcome or a collection of outcomes. Ex. Rolling a 1 or rolling an odd number.

Favorable outcomes The outcomes for a specific event. Ex. The favorable outcomes for rolling an odd number are rolling a 1, 3, or 5

Probability A number from 0 to 1 that measures the likelihood that an event will occur.

Theoretical Probability When all outcomes are equally likely, the theoretical probability is favorable possible Ex. A bag of 40 marbles contains 8 blue marbles. The theoretical probability of randomly choosing a blue marble is 8/40 = 1/5 = 0.2

Experimental Probability Based on repeated trials of an experiment. successes trials Ex. A basketball player has made 30 out of 36 attempted free throws. The experimental probability that she will make a free throw is 30/36 = 5/6 ≈ 0.83

Odds in Favor When all outcomes are equally likely, the ratio of the number of favorable to unfavorable outcomes. favorable unfavorable Ex. When you randomly choose an integer from 1 to 10, the odds in favor of choosing an integer divisible by 3 are 3/7 or 3 to 7.

Odds Against When all outcomes are equally likely, the ratio of the number of unfavorable to favorable outcomes. unfavorable favorable Ex. When you randomly choose an integer from 1 to 10, the odds against choosing an integer divisible by 3 are 7/3 or 7 to 3.

Ways to count combinations for compound events Tree Diagram and Counting Principle

Tree Diagram A diagram that uses branches to list all possible outcomes. Ex. HT HTHT possibilities: HHHTTHTT

Counting Principle Uses multiplication to determine the number of ways that two or more events can occur. Ex. You have 3 shirts and 4 pairs of pants. The total number of shirt-and- pants combinations that you can choose from is 3 4 = 12.