Wednesday, August 26, 2015

Drawing Straws with Chris and Marilyn

via WikimediaCommons

Today, Chris Harrow called attention to a Marilyn vos Savant probability problem from earlier in the month (an inquiry from a reader at Parade Magazine) that ran as follows:
"Say four people are drawing straws for a prize. My friends and I agree that the first person to draw has a 1 in 4 chance of getting the short straw. However, if he or she does get it, the second person’s chances drop to zero. And if the first person doesn’t get the short straw, the second person’s chances increase to 1 in 3, and so on. Our disagreement: Is it better to draw first, last, or does it make any difference?"
To which Marilyn simply responded:
"The order makes no difference. Envision all four people drawing straws, but instead, not looking at them yet. At this point, each person has a straw. Does it help to be the first or last one to look? No."
But Chris nicely fleshed it out a bit more as a teaching moment to make the distinction between frequentist and conditional probability; i.e. there are potentially two different probability sets here: 1) if all 4 straws are drawn and only THEN looked at, versus 2) if each straw is looked at as it is drawn:

And at the end of his post Chris makes an analogy from the straw-drawing to physics' quantum theory (or perhaps really Schrodinger's cat); I'm not sure if a physicist would be pleased with the analogy, but it's a nice thought exercise.

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