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Friday Puzzler - Presidential Deaths

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Friday Puzzler - Presidential Deaths

#1

Friday Puzzler - Presidential Deaths

Alex Y

A friend of mine from the Ukraine is a mathematics professor whose area of study is probability. He knows nothing about US history. I told him that our founding event was the Declaration of Independence, which we celebrate on July 4. I also told him that it was interesting that three of our first 5 presidents had died on July 4, and asked him what the probability of that was. He said that the mathematics to answer that was trivial, but he was not a savant, so he couldn't give me a numerical answer off the top of his head. However, he said he would give me 10 to one odds that if I told him the names of the first through the fifth president, he could name one of the three who died on the fourth of July.

How could he be so confident that he could name one of the three?

Credit to Click and Clack the Tappet Brothers, on Car Talk.

Re: Friday Puzzler - Presidential Deaths

#2

Re: Friday Puzzler - Presidential Deaths

Larry Barrett

Maybe he was going to provide two names at random, out of the five.

This problem is like the typical probability problem where you have, say, 3 black balls (3 men died on July 4) and 2 white balls (2 men did not die on the 4th) in a bag. If you draw 2 balls from the bag, what is the probability that at least one will be black (one of the two names will have died on the 4th)?

The possibilities are BB, BW, WB, WW, and the probabilities of each are

BB = 3/5 x 1/2 = 3/10

BW = 3/5 x 1/2 = 3/10

WB = 2/5 x 3/4 = 3/10

WW = 2/5 x 1/4 = 1/10

The probability of drawing two balls and having at least one be black (providing two names and having at least one who died on the 4th) is 3/10 + 3/10 + 3/10 = 9/10. So 10 to1 odds would be about right.

Click and Clack probably had a better answer.

Re: Friday Puzzler - Presidential Deaths

#3

Sorry, but no

Alex Y

He gave me only one name, and I ended up paying him $1 rather than collecting $10 :-(

Re: Friday Puzzler - Presidential Deaths

#4

Re: Friday Puzzler - Presidential Deaths

Henry Higginbotham

Maybe the same reason that no one would claim to be in the "Top 10" of something if he or she were, in fact, number 3.

Re: Friday Puzzler - Presidential Deaths

#5

Correct!

Alex Y

My friend guessed Monroe, using the logos you alluded to. The other two were Adams and Jefferson, who died on the same Fourth of July.

Unrelated to the puzzle, I worried about a hospital I saw claiming on a billboard to be "nationally ranked". Were they ranked 2,456 out of the 2,458 hospitals ranked? Kind of a vacuous claim!

👍 This page answered my questions

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