Transcript Probability
PROBABILITY Chapter 8 LEARNING TARGET I can find the probability of a simple event. DEFINITIONS An outcome is any one of the possible results of an action. A simple event has one outcome or a collection of outcomes. The chance of that event happening is called its probability. KEY CONCEPT If all outcomes are equally likely, the probability of a simple event is the ratio that compares the number of favorable outcomes to the number of possible outcomes. The probability that an event will happen can be any number from 0 to 1, including 0 and 1. Probabilities can be written as fractions, decimals, and percents. PROBABILITY NUMBER LINE 1 0 Events that are impossible have a probability of 0. Rolling a 7 with a 6-sided dice. Rolling a 7 with a 6-sided dice has a probability of 0 because it cannot happen. PROBABILITY NUMBER LINE 1 0 Events that are certain have a probability of 1. Getting wet if you walk out in a downpour with no umbrella. The probability of you getting wet in this scenario is 1. It is certain to happen. PROBABILITY NUMBER LINE 0 An event whose probability is closer to 0 is less likely to occur. 1 An event whose probability is closer to 1 is more likely to occur. WHAT IS THE PROBABILITY OF… 0 ½ 1 Having a coin land on heads. What “number” falls in the middle of 0 & 1? So, the probability of a coin landing on heads is ½. The coin is just as likely to land on heads as it is to land on tails. Events that have the same likelihood of happening fall right in the middle of 0 & 1. COMPLEMENTARY EVENTS Two events are complementary events if they are the only two possible outcomes. The sum of the probabilities of an event and its complement is 1 or 100%. In symbols, P(A) + P(not A) = 1. LEARNING TARGET I can find sample spaces and probability. DEFINITIONS The set of all the possible outcomes in a probability experiment is called the sample space. A tree diagram is a display that represents the sample space. EXAMPLE A vendor sells vanilla and chocolate ice cream. Customers can choose from a waffle or sugar cone. Find the sample space for all possible orders of one scoop of ice cream in a cone. Ice Cream Cone waffle vanilla sugar Sample Space vanilla, waffle vanilla, sugar chocolate chocolate, waffle chocolate, sugar waffle sugar LEARNING TARGET I can use multiplication to count outcomes and find probabilities. FUNDAMENTAL COUNTING PRINCIPLE If event M has m possible outcomes and event N has n possible outcomes, then event M followed by event N has m x n possible outcomes. EXAMPLE Find the total number of outcomes when a coin is tossed and a number cube is rolled. 2 x 6 = 12 2 represents the number of possible outcomes for the coin toss. 6 represents the number of possible outcomes for the number cube being rolled. LEARNING TARGET I can find the number of permutations of a set of objects. WHAT IS A PERMUTATION? A permutation is a listing of objects in which order is important. You can use the Fundamental Counting Principle to find the number of permutations. EXAMPLE You are making your schedule for your first semester of high school. Your options for classes are Biology, English, Government, and Geometry. How many different ways are there to arrange your classes? There are 4 choices for the first class. After picking your 1st class, only 3 choices remain. After picking your 1st and 2nd classes, only 2 choices remain. After picking your 1st, 2nd, and 3rd classes, only 1 choice is left. 4 x 3 x 2 x 1 = 24 ways to arrange your classes LEARNING TARGET I can find the probability of independent and dependent events. DEFINITIONS A compound event consists of two or more simple events. Compound events can be independent or dependent. With independent events, the outcome of one event does NOT affect the other event. If the outcome of one event affects the outcome of another event, the events are called dependent events. PROBABILITY OF INDEPENDENT EVENTS The probability of two independent events can be found by multiplying the probability of the first event by the probability of the second event. P(A and B) = P(A) x P(B) PROBABILITY OF DEPENDENT EVENTS To find the probability of two dependent events, you multiply the probability of the first event times the probability of the second event after the first event occurs. P(A and B) = P(A) x P(B following A)