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... where i and j denote the numbers on the two dice on the first roll, and k, ` the numbers on the two dice on the second roll. All outcomes are equally likely, so each outcome has probability 1/64 . If we place both quarters on 5, we win if the first roll of both dice sums to 5, and the second roll of ...
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... • Although the casino has the upper hand, the odds are much closer to 50-50 than with other games – Notable exceptions are games that you are not playing against the house – i.e., poker • You pay a fixed amount per hand ...
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... To find x bar (the mean of the x coordinates) take the sum of the x coordinates and divide the sum by the number of x coordinates which in this case is 4. To find y bar (the mean of the y coordinates) take the sum of the y coordinates and divide the sum by the number of y coordinates which in this c ...
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... A box contains four blue and five red discs. Two discs are drawn at random from the box. Find the probability that exactly one red disc is drawn. Solution Note : This is the same as asking the probability of drawing one red disk and one blue disk. No. of favourable outcomes: From 5 red choose 1 and ...
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Q: Roll a fair die. (a) What is the expected number of different faces

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... Discrete Random Variables and Their Probability Distributions A discrete random variable X takes a fixed set of possible values with gaps between. The probability distribution of a discrete random variable X lists the values xi and their probabilities pi: ...
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Chapter 4 Probability
Chapter 4 Probability

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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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