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Introduction. This chapter introduces students to counting techniques necessary for the study of probability. How many outcomes are possible when rolling two dice? when flipping four coins? when drawing five cards from a deck of 52?
Creating a table can help you solve probability problems. You are to choose one of the cards at right without looking. Consider the probability of three outcomes: 1) choosing a vowel,
• Probability theory provides the mathematical rules for assigning probabilities to outcomes of random experiments, e.g., coin flips, packet arrivals, noise voltage • Basic elements of probability:
In order to describe an unfair die properly, we must specify the probability for each of the six possible outcomes. The following table gives answers for each of 4 different dice.
Practice Problems in Probability. Easy and Medium Di culty Problems. Problem 1. Suppose we ip a fair coin once and observe either T for \tails" or H for \heads." Let X1 denote the random variable that equals 0 when we observe tails and equals 1 when we observe heads. (This is called a Bernoulli random variable.)
understand the basic concepts of probability theory, including independence, con-ditional probability, Bayes’ formula, expectation, variance and generating func-tions; be familiar with the properties of commonly-used distribution functions for dis-crete and continuous random variables; understand and be able to apply the central limit theorem.
Probability gives a measure of how likely it is for something to happen. It can be defined as follows: Definition of probability: Consider a very large number of identical trials of a certain process; for example, flipping a coin, rolling a die, picking a ball from a box (with replacement), etc. If the probability of a particular event
