Probability

Rolling Dice: Three Probability Problems

Last week we examined three probability problems that had problems. Looking further back, I find that Jonathan, who asked the first of those questions, asked a group of questions about rolling multiple dice in 2022. They provide some additional lessons about easy mistakes to make.

How to Think Through Probability Problems

It’s been a while since we’ve looked at probability. Here, we’ll look at three questions that we received last year. In each case, we have to detect an error! They’re good examples of what can go wrong, and what to do when your answer appears to be wrong.

Permutation vs Combination: Clarifying Our Terms

A couple recent questions dealt with details in the way permutations and combinations are explained. What do we mean when we say that “order matters” for a permutation, and that there is “no repetition” or that the things being chosen are “different”? Teachers need to know how students hear such words.

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.

Slow and Fast Ways to Solve a Probability Problem

Last week’s discussion reminded me of another question, from July, about a probability problem that was solved in a hard (but educational) way and an easy way. This instance is more extreme, and, due to its length, requires extreme editing in order to fit here.

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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