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View Poll Results: Which is the correct outcome on average? | |||
THT and THH need the same number of coin tosses |
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6 | 50.00% |
THT sequence needs more coin tosses |
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5 | 41.67% |
THH sequence need more coin tosses |
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1 | 8.33% |
Voters: 12. You may not vote on this poll |
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#1 |
The Grand Mouse 高貴的老鼠
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Finding Sequences Puzzle
Here's a Simple Probability Puzzle, taken from http://toshuo.com/2007/a-simple-probability-puzzle/
You are monitoring an automatic coin flipping machine. It flips a coins every second, and you can see whether the coin lands show Heads (H) or Tails (T). You will be looking for non-overlapping sequences of three results. For instance, if you were looking for HTH, the sequence THTHTHHHTHTT would have only two HTH sequences in it (bold) THTHTHHHTHTT. Your first task is to keep watch until 10 sequences of THT have appeared. After you've seen the 10th THT sequence, you note the total number of coin tosses you've observed while monitoring for THT Once you've spotted 10 sequences of THT, you start monitoring again with the next coin toss after the last T of your tenth THT sequence. This time you're looking for sequences of THH. Again, after you've seen the 10th THH sequence, you note the total number of coin tosses you've observed while monitoring for THH. The coin tossing machine is fair (H 50%, T 50%) and random. You are vigilant, and do not make any mistakes in your monitoring of the coin tosses. On average, will the number of coin tosses you observe while monitoring for THT be greater, the same or less than the number of coins tosses you observe while monitoring for THH? Please vote! You may also give an argument for your vote in comment, in Spoiler:
please.
Last edited by pdurrant; 07-27-2010 at 04:45 AM. Reason: edited for clarity |
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#2 |
Wizard
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Spoiler:
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#3 |
The Grand Mouse 高貴的老鼠
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Let me clarify. There is no overlap in the sequences, even when going from one task to the next. When you finish monitoring for THT, you start monitoring for THH starting with the next coin toss, not the last one of THT. (Question edited to clarify this point.) |
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#4 | |
Addict
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Quote:
Spoiler:
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#5 |
Addict
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Spoiler:
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#6 |
Guru
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The answer is in the blog linked in the first post, and Lo Zeno got it right.
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#7 |
The Grand Mouse 高貴的老鼠
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#8 |
The Grand Mouse 高貴的老鼠
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#9 |
The Grand Mouse 高貴的老鼠
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#10 |
Addict
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I solved it because that puzzle is very, very similar to one that my statistics & probability teacher at university made us solve
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#11 |
The Grand Mouse 高貴的老鼠
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Once the poll closes on Monday, I'll post the answer, a verbal explanation, and mathematical way to calculate the answer.
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#12 |
The Grand Mouse 高貴的老鼠
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#13 |
The Grand Mouse 高貴的老鼠
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Answer:
Spoiler:
A bare answer doesn't really help those of you who got the answer wrong. Here's an explanation Spoiler:
and an analysis. Spoiler:
Whew! Hopefully I haven't made too many typos in that! |
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