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Understanding Probability in Finite Sample Spaces with Poker Hand Examples

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This document explores probability theory, focusing on finite sample spaces with equally likely outcomes. It defines key concepts such as events, complementary events, and their probabilities—illustrated with practical examples involving five-card poker hands. Examples include calculating the probability of specific cards, combinations, and outcomes like having at least one ace or achieving a flush. Furthermore, it addresses lottery probabilities involving the selection of integers, providing insights into fundamental probability principles applicable in various contexts.

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Understanding Probability in Finite Sample Spaces with Poker Hand Examples

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  1. 6.1 Probability exercises

  2. Def • Def: If S is a finite sample space of equally likely outcomes, and E is an event, that is, a subset of S, then the probability of E is P(E)= |E|/|S|. • Thm. 1: Let E be an event in a sample space S. The probability of the event , the complementary event of E, is given by P( ) = 1- P(E).

  3. Ex • Ex. 1: What is the probability that a five-card poker hand contains the ace of hearts? • Ex. 2: What is the probability that a five-card poker hand contains the two of diamonds and the three of spades? • Ex 3: What is the probability that a five-card poker hand contains exactly one ace?

  4. Ex • Ex 4 What is the probability that a five-card poker hand contains at least one ace? • Ex 5: What is the probability that a five-card poker hand contains a flush, that is, five cards of the same suit? • Ex 6: Find the probability of winning the lottery by selecting the correct six integers, where the order in which these integers are selected doesn’t not matter, from the positive integers not exceeding 36.

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