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MAS 108 Probability I
MAS 108 Probability I

... Let N be the random number shown on the die, and X the number of heads. It is possible to calculate the p.m.f. of X directly, though it is quite a lot of work. For example, what is the probability that X = 5? This can only occur if either N = 5 and we get heads five times (with probability (1/6) × ( ...
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... Chapter 2: Probability The aim of this chapter is to revise the basic rules of probability. By the end of this chapter, you should be comfortable with: • conditional probability, and what you can and can’t do with conditional expressions; • the Partition Theorem and Bayes’ Theorem; • First-Step Anal ...
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... • A different way to conduct the study would be to measure the time (in hours) a salesperson spends making calls in one day. Because the time spent making sales calls can be any number from 0 to 24 (including fractions and decimals), x is a continuous random variable. You can represent its values wi ...
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... We know that about 68% of samples will give between 11.33 (=15 - 3.67) and 18.67 (= 15 + 3.67) people with allergies; about 95% will give between 7.66 (= 15 - 2*3.67) and 22.34 (= 15 + 2*3.67) people with allergies. (c) A sample with 30 allergy sufferers would be unusual – 30 is more than µ + 2σ (wh ...
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... Fort Myers and Miami on a Florida state map. The string distance was 7.75 inches, which represents a real-life distance of about 155 miles. Another group measured the distance between Tampa and Orlando on the same map and found that distance to be 4.25 inches. What is the real-life distance to the n ...
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... A firm has developed a new product (called X). Now, they can either test the market or abandon the project. The details are set out below. Test market costs = €50,000; likely outcomes are favourable (P=0.7) or failure (P = 0.3). If favourable, the firm could either abandon or produce it where demand ...
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Introduction to Probability - Finite Mathematics Section 6.2

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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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