1. Lesson 6.6 Probability Students will be able to determine theoretical probabilities.

2. The study of probability helps us figure out the likelihood of something happening. For instance, when you roll a pair of dice, you might ask how likely you are to roll a seven. In math, we call the "something happening" an "event." The probability of the occurrence of an event can be expressed as a fraction or a decimal from 0 to 1. Events that are unlikely will have a probability near 0, and events that are likely to happen have probabilities near 1. What is the probability that you roll a seven with this “one” die? zero What is the probability that you will roll a seven with “one” of these octahedron dice? 1 8 Or.125

3. Probability is measured on a scale from 0 to 1. P = 0 Impossible P = 0.25 Not likely P= 0.5 Likely to occur Half of the time P = 0.75 Quite likely P= 1 Certain In any probability problem, it is very important to identify all the different outcomes that could occur. For instance, in the question about the dice, you must figure out all the different ways the dice could land, and all the different ways you could roll a seven. Total number of possibilities when you roll this die: 1, 2, 3, 4, 5, 6. The total number of possible outcomes with this die is: 6 The total number of possible outcomes with an octahedron is-- 8

4. A cube contains 15 marbles: 6 red, 4 blue, 5 green. You choose one marble at random. Find the probability that it is red. To find a basic probability with all outcomes equally likely, we use a fraction: number of favorable outcomes Probability of event total number of possible outcomes Number of favorable outcomes = how many red marbles are there in the cube? Total number of possible outcomes= how many marbles are in the cube? 6 15 Probability of choosing red = 3 3 2525 You do remember how to turn a fraction into a decimal! =.4

5. Find the probability if you spin the spinner once. P(red) P(brown or yellow) P(yellow) P(green) Remember: Probability of event= Number of favorable outcomes Total number of outcomes 1 8 OR.125 3 8 OR.375 2 1 8 4 OR.25 4 1 8 2 OR.5

6. Paul has 20 t-shirts in his closet. 3 green, 4 red, 5 white, and 8 blue. If Paul chooses a t-shirt without looking what is the probability that it will be: Blue = Green = White or Blue = This is an actual “state exam” released question. It was on the 2003 California state exam. 8 2 20 5 OR 0.4 3 20 OR 0.15 5 + 8= 13 20 OR 0.65