MAT 142 Lecture Video Series. Combinatorics and Probability.

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MAT 142 Lecture Video Series

Presentation transcript:

MAT 142 Lecture Video Series

Combinatorics and Probability

Objectives Determine the probability of event where the probability requires using combinations, permutations and/or fundamental counting principle

One 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 Cards

A full house in poker is a 5-card 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 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 University