Comments on: A Simple Probability Puzzle

By: Mark

Mark — Thu, 29 Nov 2007 18:18:02 +0000

See the follow-up post. It goes through how to calculate them exactly.

http://toshuo.com/2007/even-simple-probabilty-puzzles-can-be-tricky/

By: JD Huntington

JD Huntington — Wed, 28 Nov 2007 22:36:12 +0000

FYI: The rough probabilities for all 8 three coin flips are as follows:


(((H H H) 13.76811111111111)
 ((H H T) 8.067777777777778)
 ((H T H) 9.979)
 ((H T T) 8.085888888888888)
 ((T H H) 8.022222222222222)
 ((T H T) 9.956666666666667)
 ((T T H) 7.963111111111111)
 ((T T T) 14.158444444444445))

By: Michael Turton

Michael Turton — Tue, 27 Nov 2007 05:37:13 +0000

Very interesting puzzle, Mark. Very enjoyable.

Michael

By: Even Simple Probabilty Puzzles Can Be Tricky | Doubting to shuo: Chinese, Investing, EFL and Being a Geek in Taiwan

Mon, 26 Nov 2007 22:33:08 +0000

[...] votes from Friday’s Simple Probability Puzzle are in. Here was the question: Imagine there’s a completely random event with two outcomes, say [...]

By: Mark

Mark — Mon, 26 Nov 2007 16:31:34 +0000

Wayne, Sam’s comment #23 might be what you’re looking for. It’s a mathematical derivation of how many flips it will take to get the sequence

By: Giavasan » Un semplice quiz sulle probabilità

Giavasan » Un semplice quiz sulle probabilità — Mon, 26 Nov 2007 05:53:52 +0000

[...] Link: A Simple Probability Puzzle. [...]

By: wayne

wayne — Mon, 26 Nov 2007 05:46:13 +0000

I was trying to wrack my brain trying to think of how to mathematically derive the average number of flips it would require to get to THT or THH, but I couldn’t come up with anything. I agree with Robin’s intuition and the brute force Monte Carlo program bears out that reasoning, but that’s not enough.

Anyhow, I guess you could state that for any sequence of heads and tails aBc (where a and c denote one head or tail and B denotes any number of heads and tails), you will reach a1Bc1 before a2Bc2 if a1 doesn’t equal c1 and a2 equals c2.

For instance, you will reach THHHHHHHHHH in a fewer number of flips than you will reach THHHHHHHHHT.

By: Mark

Mark — Sun, 25 Nov 2007 19:55:53 +0000

I’ll keep your offer in mind. Thanks! It sounds like you’ve basically got it. Another way of thinking of your analogy would be this:

1. Start with THH. Flip until you get THT.
2. Start with THT, flip until you get THH, or HH right away (since you’ve already got the initial T)

Which takes longer?

By: Tim Mitchell

Tim Mitchell — Sun, 25 Nov 2007 19:19:11 +0000

Mark,

Not trying to be a pain, honest. I’ve enjoyed toying with this puzzle, even when I misunderstood.

See if I get the problem with this description (note that I’m still starting with THH and THT as givens for the beginning of the sequences. If that doesn’t work out, I’m still missing something).

1. Start with THH. Flip until you get THT.
2. Start with THT, flip until you get THH.
Which sequence will, on average, be longer?

If I’m stating it correctly, then THH to THT will be the longer sequence on average. Starting with THT, it’s possible to get your “TH” on the next flip, whereas it’s impossible starting with THH.

I know I’m way past the point of telling my wife, “Well, I’m off to Taipei for a free beer!” But if you’re ever in Minneapolis, I’ll buy you an entire dinner.

Even when I’m wrong, I have fun.

By: william

william — Sun, 25 Nov 2007 17:25:24 +0000

any specific three-toss pattern will happen with the same average number of tosses. tails tails tails the same as heads tails heads, whatever. it is 2 x 2 x 2 =ing 8 tosses on average for each pattern. kissy