Real life

Probability of Consecutive Numbers in a Lottery

A recent question about lottery numbers reveals that a seemingly special event is in fact surprisingly common: namely, the presence of consecutive numbers in a lottery drawing. The calculation is an interesting one, and we’ll also see a way to check our answer, then compare it to reality.

Diluting a Solution: Math vs. Reality

Here is a little question about making a formula to dilute a solution; we’ll see how to do the algebra, and also how what we teach in math classes isn’t quite real.

The Book Stacking Problem

(An archive question of the week) A recent question asked about a well-known problem about stacking books (or cards, or dominoes) so that the top one extends beyond the base, giving a link to one of many explanations of it – but one, like many, that doesn’t quite fill in all the details. Doctor Rick …

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How Risks Add Up

(A new question of the week) Real life questions of probability often require information that we don’t have – they become a job for statistics instead. But sometimes just trying some plausible numbers, as in a Fermi problem, can yield interesting results. Here we consider the probability of an injury when kids play near a …

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A Tunnel Through the Earth

I have a very short problem this week: How deep will you go if you dig a straight tunnel through the earth, how long will it be, and what angle do you have to start at?

Distances on Earth 3: Planar Approximation

We’ve looked at two formulas for the distance between points given their latitude and longitude; here we’ll examine one more formula, which is valid only for small distances. This is a “flat-earth approximation” to distance.

How Much Does the Earth Curve?

We’ve looked at how to find the circumference of the earth, and how far we can see over the horizon. Another kind of question we’ve had about the curvature of the earth is, how much does it curve over a given distance? That has been asked in several different ways, which lead to some intriguing …

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How Far Can I See?

We have been looking at questions about the roundness of the earth, starting with the general fact, and then the determination of the size of the earth. A very common question is about how that roundness affects what we can see, sometimes as a challenge (“If I can see this, then how can the earth …

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