MAT 142 Lecture Video SeriesCombinatorics and ProbabilityObjectivesOne type of lottery is the 6/49 lottery (the player selects any 6 of the numbers from 1 to 49).A group of 60 people is selected at random. What is the probability that at least two of them will have the same birthday?Two hundred people apply for three jobs. Seventy of the applicants are women.Slide 7A full house in poker is a hand with three of a kind and a pair (two of a kind).Keno is a lottery-like casino game. There are 80 balls numbered 1 through 80. A player picks a specified number of spots (1 through 80) on her card. The casino picks 20 of the 80 balls. The player wins when a specified number of her “spots” (numbers) or more are included in the 20 numbered balls that the casino picks.In our Keno game, the player picks 6 spots. She wins if 4 or more of her spots are selected by the casino.Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State UniversityMAT 142Lecture Video SeriesCombinatorics and ProbabilityObjectives•Determine the probability of event where the probability requires using combinations, permutations and/or fundamental counting principleOne type of lottery is the 6/49 lottery (the player selects any 6 of the numbers from 1 to 49). a. Find the probability of winning first prize (your selection of six numbers matches the six winning numbers.b. Find the probability of winning second prize (you select five of the six winning numbers).A group of 60 people is selected at random. What is the probability that at least two of them will have the same birthday?Two hundred people apply for three jobs. Seventy of the applicants are women. a. If three persons are selected at random, what is the probability that all are women? b. If three persons are selected at random, what is the probability that exactly two are women?c. If three persons are selected at random, what is the probability that only one is a woman?d. If three persons are selected at random, what is the probability that none is a women?Standard Deck of CardsA full house in poker is a hand with three of a kind and a pair (two of a kind). a. What is the probability of being dealt an “aces over kings” full house? b. How many different types of full houses are there?c. What is the probability of being dealt a full house?Keno is a lottery-like casino game. There are 80 balls numbered 1 through 80. A player picks a specified number of spots (1 through 80) on her card. The casino picks 20 of the 80 balls. The player wins when a specified number of her “spots” (numbers) or more are included in the 20 numbered balls that the casino picks.In our Keno game, the player picks 6 spots. She wins if 4 or more of her spots are selected by the casino. a. What is the probability of 6 winning spots?b. What is the probability of 5 winning spots?c. What is the probability of 4 winning spots?d. What is the probability of winning?Creator and ProducerElizabeth Jones forThe School of Mathematical and Statistical SciencesatArizona State University VideographerMike Jones©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State
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