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35 replies to this topic

### #1 bonanova

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Posted 10 October 2008 - 07:21 AM

Here's a simple question about probability and expectation.

On average, how many times do you need to flip a fair coin
before you have seen a run of an odd number of heads,
followed by a tail?

This puzzle was submitted, but not used, in the International
twenty-five years ago. What makes it
appealing for use as a test question [where time can be of the
essence] is that it has an easy answer as well as a difficult answer.

That is it tests for insight.
As such it qualifies as a puzzle as well as a math question.

Extra bragging rights go to the solver who solves it both ways.
• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #2 woon

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Posted 10 October 2008 - 07:57 AM

Here's a simple question about probability and expectation.

On average, how many times do you need to flip a fair coin
before you have seen a run of an odd number of heads,
followed by a tail?

This puzzle was submitted, but not used, in the International
twenty-five years ago. What makes it
appealing for use as a test question [where time can be of the
essence] is that it has an easy answer as well as a difficult answer.

That is it tests for insight.
As such it qualifies as a puzzle as well as a math question.

Extra bragging rights go to the solver who solves it both ways.

Must the tail also in odd number? :huh
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### #3 nobody

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Posted 10 October 2008 - 08:52 AM

Spoiler for Let me try it

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### #4 igor

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Posted 10 October 2008 - 09:30 AM

Spoiler for could it be?

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### #5 Yoruichi-san

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Posted 10 October 2008 - 09:40 AM

Spoiler for Let me try it

Spoiler for I think you're forgetting...

Spoiler for Or...

Edited by Yoruichi-san, 10 October 2008 - 09:47 AM.

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

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Chromatic Witch links now on my 'About Me' page!  Episode 2 is awaiting it's epic conclusion...are you up to the task?

When life hands me lemons, I make invisible ink.

### #6 aussietony

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Posted 10 October 2008 - 09:53 AM

first flip a head second flip a tail will make the eqution true. But that is only one solution.
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### #7 nobody

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Posted 10 October 2008 - 10:10 AM

Spoiler for I think you're forgetting...

Spoiler for Or...

You're right Yourichi-san, I calculated the probability of getting a tail before an odd number of heads. But it was not the question
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### #8 bonanova

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Posted 10 October 2008 - 10:37 AM

Must the tail also in odd number? :huh

Here are some examples of what you want to have happen.
It should clear up what the OP asks:

Here the dots represent H or T but with the caveat that
the dots don't contain the string of results you want.

. . . . H H H T [8 tosses]
. . . . . . . H H H H H T [13 tosses]
H T [2 tosses]
• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #9 octopuppy

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Posted 10 October 2008 - 10:51 AM

Here are some examples of what you want to have happen.
It should clear up what the OP asks:

Here the dots represent H or T but with the caveat that
the dots don't contain the string of results you want.

. . . . H H H T [8 tosses]
. . . . . . . H H H H H T [13 tosses]
H T [2 tosses]

I'm confused. What if you tossed:
T H H T
Would that count as a success? That includes the string "H T" but is preceded by another head. Technically it meets the criteria but I suspect that wasn't what you meant...
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### #10 woon

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Posted 10 October 2008 - 10:55 AM

Here are some examples of what you want to have happen.
It should clear up what the OP asks:

Here the dots represent H or T but with the caveat that
the dots don't contain the string of results you want.

. . . . H H H T [8 tosses]
. . . . . . . H H H H H T [13 tosses]
H T [2 tosses]

Spoiler for then if I am not mistaken

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