PPT-Independent Events

Examples of independent events You flip a coin and get a heads  and  you flip a second coin and get a tails  The two coins dont influence each other The probability of rain today . What are the odds?. To find the probability that a man has both a beard and a mustache would you multiply the probability of a man having a beard by the probability of a man having a mustache?. D. ependent Events. Up #24. Write each answer as a ratio, as a decimal, and as a percent.. A 1–6 number cube is rolled.. 1.. What is the probability . of getting an even number?. 2.. What is the probability that the number will . Unions and Intersections. When you consider all the outcomes for either of two events, A and B, you form the . union. of A and B.. When you consider only the outcomes shared by both A and B, you form the . http://mikeess-trip.blogspot.com/2011/06/gambling.html. 1. Uses of Probability. Gambling. Business. Product preferences of consumers. Rate of returns on investments. Engineering. Defective parts. Physical Sciences. Laws of. Probability. Exhaustive events. When a normal, unbiased, 6-sided die is thrown, the numbers 1 to 6 are possible.. These are the ONLY ‘events’ possible.. This means these are EXHAUSTIVE as they cover ALL POSSIBLE OUTCOMES.. Section 5.1. An event is the set of possible outcomes. Probability is between 0 and 1. The event A has a complement, the event not A. Together these two probabilities sum 1.. . ex. At least one and none are complements. Independent and Dependent Events. Independent . Events. Frequently you will determine the probability of multiple events. You’ll need to decide if the events are independent events or dependent events.. and are dependent otherwise. . The definition implies that B is independent of A as well, for if A is independent of B,. 2. Example. Consider a gas station with six pumps numbered 1,2,…,6, and let denote the simple event that a randomly selected customer uses pump j, j=1, …,6. Suppose that , . The probability that events . A. and . B. both occur can be found using the . general multiplication rule. P. (. A . ∩. . B. ) = . P. (. A. ) • . P. (. B . | . A. ). where . P. (. B . | . A. ) is the conditional probability that event . whether events are independent or dependent.. Apply the rules of probability to determine the probability of an event. .. Independent Events . Events where the outcome of one . does not . affect the probability of the other are called . Essential Question: How do you find the probability of compound events?. Before we start…. Suppose you randomly select a classmate. Event . A. is selecting a . female. student and event . B. is selecting a student with . Section 5.1. How Probability Quantifies Randomness. Probability—outline:. I Introduction to Probability. A Satisfactory outcomes vs. total outcomes. B Basic Properties. C Terminology. II Combinatory Probability. Independent Events. 4. Use the multiplication rule for independent events to calculate probabilities.. Calculate . P. (at least one) using the complement rule and the multiplication . rule for . independent events.. Third. Edition, By Michael Baron. Chapter 2: Probability. CIS 2033. Computational Probability and Statistics . Pei Wang. Events and probability. Intuitively speaking, the . probability. of an event is its .