Fractions and Felonies

(A new question of the week) A recent question involved a word problem about fractions, which will fit in nicely with the current series on fractions. We’ll explore several ways to solve a rather tricky fraction word problem, some avoiding fractions as much as possible, some focusing on the meaning of the fractions, and others …

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Interpreting Probability Questions

(A new question of the week) A couple recent questions centered around how to interpret probability problems, whose wording can often be subtle, and whose solutions require care.

Polygons and Handshakes

We’ll spend the next couple weeks looking at various counting problems. This topic, called combinatorics, is often studied along with probability, but many of the topics we’ll see here feel more like geometry problems! Here, we’ll be counting the diagonals of a polygon, and handshakes between people at a party. Counting diagonals We’ll start with …

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Bayes and Virus Testing

News about testing for viruses has reminded me of a couple problems that I linked to some time ago, but never dealt with directly. The question is, given data such as the result of a (fallible) blood or swab test, how sure can we be of the results? The answer is sometimes surprising. False positives …

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Rank of a Binary Number

(A new question of the week) A few months ago, I wrote about Ranking a Word Among Its Permutations, that is, finding where a word would be found in an ordered list of all possible “words” made by permuting its letters. The problem in general requires a (sometimes lengthy) algorithm. A month or so later, …

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More About Independent Events

Last time, we looked at the basic definition of independent events. This time I want to explore some deeper questions about the concept. Independence by the numbers We’ve seen that, informally, we think of independent events as not affecting one another’s probabilities. Mathematically, though, independence is defined by the fact (which is implied by that …

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