Browsing category probability

Heads, Tails and bumps-a-daisy

It’s always Alice and Bob. Why must it always be Alice and Bob? In any case, the two of them are tossing coins Until they hit a particular sequence: Alice until she hits a head then a tail, Bob until he hits two heads in a row. Counter-intuitively, Alice will

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A probability puzzle

A nice prompt from @shahlock, some time ago: Math Prompt #apstats #mtbosTwo players A, B. A is 4-0 against B. How would you estimate probability A wins next match? Assume independence — M Shah (@shahlock) November 27, 2016 Stand back, everyone: I’m going to apply Bayes’s Theorem. A prior Let’s

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Two coins, one fair, one biased

When the redoubtable @cuttheknotmath (Alexander Bogomolny) poses the following question: Two Coins: One Fair, one Biased #FigureThat #math #probability — Alexander Bogomolny (@CutTheKnotMath) March 5, 2018 … you know there must be Something Up. Surely (the naive reader thinks) the one with two heads out of three is

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The Mathematical Ninja and the SSNs

A professor – according to Reddit – asked their class how many people you’d need to have in a room to be absolutely certain two of them would have Social Security numbers1 ending in the same four digits (in the same order). 10001, obviously. How about a probability of 99.9%?

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Sprinkle on the sugar, eat the lot

A Christmas Pudding Puzzle I swear, this one came up in real life! My partner made a Christmas pudding for the most recent festive season. Delicious, it was. When it was about half-eaten, I went to microwave a portion. “Hang on,” she said: “there might be a coin in there.”

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The Paradox of the Second Ace

This post is inspired by a Futility Closet article. Do visit them and subscribe to their excellent podcast! Suppose you're dealt a bridge hand1, and someone asks whether you have any aces; you check, and yes! you find an ace. What's the probability you have more than one ace? This

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An Australian Dining Phenomenon

In an early draft of my forthcoming book, The Maths Behind, which will be available wherever good books are sold from September, I believe, I took the following unprovoked dig at Australia: "… it crashed into the ocean about 1,600 miles to the west of Perth, Australia. There's nothing there.

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Collecting coupons

For all the grief I give @reflectivemaths on Wrong, But Useful, he does occasionally ask an interesting question. In episode 45, he wondered how many packs of Lego cards one would need to acquire, on average, to complete the set of 140?1 A simpler case Suppose, instead of 140 cards,

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A coin sequence conundrum

Zeke and Monty play a game. They repeatedly toss a coin until either the sequence tail-tail-head (TTH) or the sequence tail-head-head (THH) appears. If TTH shows up first, Zeke wins; if THH shows up first, Monty wins. What is the probability that Zeke wins? My first reaction to this question

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An ex-Formula 1 driver asks… why does nobody ever ask me my opinion?

Former Formula 1 driver @MBrundleF1 asks: These election opinion polls. I've never been approached, nor has anybody I know, about a poll on anything whatsoever. Who are these people? — Martin Brundle (@MBrundleF1) April 5, 2015 (Obviously, he didn’t ask me specifically, but I thought it was a good question.)

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