An Introduction to Probability 12.3

Vocabulary Probability – a number between 0 and 1 that indicates the likelihood an event will occur. Experimental Probability – a calculation of the probability of an event based on performing an experiment, a survey, or looking at the history of an event. Geometric Probability – a type of probability found by calculating a ratio of lengths, areas or volumes.

Probability P = ½ Event is equally likely to occur or not occur P = 1 Event is certain to occur P = 0 Event will not occur

The Theoretical Probability of an Event When all outcomes are equally likely, the theoretical probability that an event A will occur is: number of outcomes of A total number of outcomes The theoretical probability of an event is often simply called the probability of the event.

Example 1: Finding Probabilities of Events A standard deck of cards has 52 playing cards. Find the probability of drawing a king. A spinner has 8 equal-size sectors numbered 1 to 8. Find the probability of spinning a 6. Find the probability of spinning a number greater than 5.

Example 2 There are 20 students in your gym class. Your teacher divides the class into two equal softball teams. Your teams draws names one by one to determine the batting order. What is the probability that 1 of the 7 freshmen of the team will be chosen first, in any order?

Example 2 Continued There are 9 students on the math team. You draw their names one by one to determine the order in which they answer questions at a math meet. What is the probability that 3 of the 5 seniors on the team will be chosen last, in any order?

Example 3: Finding Experimental Probability Ninth graders must enroll in one math class. The enrollment of ninth grade students during the previous year are shown in the bar graph. Find the probability that a randomly chosen student from this year’s ninth grade class is enrolled in A) Consumer’s Math and B) Algebra 1 or Intro to Algebra.

Example 4: Geometric Probability You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. Are you more likely to get 15 points or 10 points? 12 inches—red(10 points) 8 inches – yellow(15 points) 4 inches-gray(20 points)