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What is Probability? Experimental Probability Theoretical Probability Independent Events Dependent Events Combinations Permutations • Probability is the possibility that a certain event will occur. An event that is certain to occur has a probability of 1. An event that cannot occur has a probability of 0. Therefore, the probability of an event occuring is always between 0 and 1. • A cross product is the product of the numberator in one ratio and the denominator in the other ratio. 1 4 1 2 3 4 3 5 6 10 = 5 • 6 = 30 3 • 10 = 30 Impossible Unlikely Likely Certain As likely as not 1 0 1 0.75 100% 75% 0.50 50% 0.25 25% 0% 0 • Experimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. • Probability is based on whether events are dependent or independent of each other. An independent event refers to the outcome of one event not affecting the outcome of another event. • A combination is an arrangement of objects or events in which order does not matter. • The number of ways that an event can occur depends on the order. • A permutation is an arrangement of objects or events in which order matters. There are 3 possible letter combinations: DG, OD & GO Example: How many different combinations can be made when picking 2 letters out of the word DOG? Example: Arrange 3 students in 3 chairs. • A dependent event is when the outcome of one event does affect the outcome of the other event. • Theoretical probability is the probability that a certain outcome will occur based on all the possible outcomes. P (a and b) = P (a) • P (b) P (a and b) = P (a) • P (b after a) 3 • 2 • 1 or 3! = 6 number of times an event occurs total number of trials Experimental Probability number of favorable outcomes total number of possible outcomes Theoretical Probability Probability of two independent events Probability of two dependent events probability of both events probability of first event probability of second event probability of both events probability of first event probability of second event Cross out duplicates. DO DG OD OG GD GO D O G 3 2 1 3 • 2 • 1 3 • 1 • 2 2 • 3 • 1 2 • 1 • 3 1 • 2 • 3 1 • 3 • 2 fraction decimal percent • • • • • • • • • • • • © Copyright NewPath Learning. All Rights Reserved. 93-4707 www.newpathlearning.com Introduction to Probability

\|xiBAHBDy01673rzu What is Probability? Experimental Probability Theoretical Probability Independent Events Dependent Events Combinations Permutations • Probability is the possibility that a will occur. An event that is certain to occur has a probability of . An event that cannot occur has a probability of . Therefore, the probability of an event occuring is always between and . • Experimental probability is ____________ _______________________________________ ______________________________________. • Probability is __________________________ _______________________________________ _______________________________________ ______________________________________. • A combination is ______________________ _______________________________________ ______________________________________. • The number of ways that an event can occur depends on the order. • A permutation is ______________________ ______________________________________. There are 3 possible letter combinations: DG, OD & GO Example: How many different combinations can be made when picking 2 letters out of the word DOG? Example: Arrange 3 students in 3 chairs. • A dependent event is __________________ _______________________________________ _______________________________________ ______________________________________. • Theoretical probability is ______________ _______________________________________ ______________________________________. P (a and b) = P (a) • P (b) P (a and b) = P (a) • P (b after a) 3 • 2 • 1 or 3! = 6 number of times an event occurs total number of trials Experimental Probability number of favorable outcomes total number of possible outcomes Theoretical Probability Probability of two independent events Probability of two dependent events probability of both events probability of first event probability of second event probability of both events probability of first event probability of second event Cross out duplicates. D O G 3 2 1 3 • 2 • 1 3 • 2 • 1 3 • 2 • 1 3 • 2 • 1 3 • 2 • 1 3 • 2 • 1 1 4 1 2 3 4 Impossible Unlikely Likely Certain As likely as not 1 0 0% 0 fraction decimal percent © Copyright NewPath Learning. All Rights Reserved. 93-4707 www.newpathlearning.com Introduction to Probability Key Vocabulary Terms • certain • combination • dependent event • event • experimental probability • favorable outcome • impossible • independent event • likely • outcome • permutation • possible outcome • probability • theoretical probability • unlikely