Posts from September 2014 (43)

In this week’s Slate Money podcast (starting at about 2:50), there’s an example of a probability puzzle that mathematically trained people tend to get wrong.  In summary, the story is

You’re at a theatre watching a magician. The magician hands a pack of cards to one member of the audience  and asks him to check that it is an ordinary pack, and to shuffle it. He asks another member of the audience to name a card. She says “Ace of Hearts”.  The magician covers his eyes, reaches out to the pack of cards, fumbles around a bit, and pulls out a card. What’s the probability that it is the Ace of Hearts?

It’s very tempting to say 1 in 52, because the framing of the puzzle prompts you to think in terms of equal-probability sampling.  Of course, as Felix Salmon points out, this is the only definitively wrong answer. The guy’s a magician. Why would he be doing this if the probability was going to be 1 in 52?

With an ordinary well-shuffled pack of cards and random selection we do know the probability: if you like the frequency interpretation of probability it’s an unknown number quite close to 1 in 52, if you like the subjective interpretation it should be a distribution of numbers quite close to 1 in 52.

With a magic trick we’d expect the probability (in the frequency sense) to be close to either zero or one, depending on the trick, but we don’t know.  Under the subjective interpretation of probability then you do know what the probability is for you, but you’ve got no real reason to expect it to be similar for other people.

Each week, we would like to invite readers of Stats Chat to submit nominations for our Stat of the Week competition and be in with the chance to win an iTunes voucher.

Here’s how it works:

• Anyone may add a comment on this post to nominate their Stat of the Week candidate before midday Friday September 5 2014.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of August 30 – September 5 2014 inclusive.
• Quote the statistic, when and where it was published and tell us why it should be our Stat of the Week.

Next Monday at midday we’ll announce the winner of this week’s Stat of the Week competition, and start a new one.

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If you’d like to comment on or debate any of this week’s Stat of the Week nominations, please do so below!