83
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64
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100 pieces 1 opportunity, choose wisely!
What you're missing here is the chance of playing at all, given that the game ends when someone finds the prize. (or, chance of finding a prize goes to 0, which is the same thing)
...
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54
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Deceptive dice game
You can make arbitrarily large sets of dice with this property.
Start with Efron's dice:
A: 4, 4, 4, 4, 0, 0
B: 3, 3, 3, 3, 3, 3
C: 6, 6, 2, 2, 2, 2
D: 5, 5, 5, 1, 1, 1
A beats B, B beats C, C ...
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45
votes
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2 Monkeys on a computer
(a) I claim that the expected typing length are the same for both monkeys. I guess something in my argument will be incorrect, as jafe's answer has 9 approvals, but finding that incorrectness would be ...
- 566
43
votes
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How many tries to roll a 6?
The answer is indeed...
...because the question is equivalent to...
Calculations:
- 21.9k
43
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Monty Hall Revisited: Winning Both Goats!
Leaving aside the dubious assumption that Monty is entirely on the up-and-up...
- 2,772
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How many tries to roll a 6?
This surprisingly beguiling puzzle may also be solved
with a surprisingly unsophisticated approach.
Symmetry, by itself, predicts the average length of
evens-only sequences ending with 6 to ...
- 21.9k
40
votes
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37
votes
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37
votes
36
votes
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35
votes
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Simulating an unbiased coin with a biased one
One possibility:
This works because:
EDIT: Inspired by @trolley813's answer here is a way to recycle the rejected entropy:
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33
votes
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How to simulate one die with three dice?
I believe this set of dice satisfies all your requirements:
- 148k
32
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28
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Coin Game with infinite paradox
OK, let's actually take this seriously. As others have said, this is the so-called St Petersburg paradox, and the reason it isn't really much of a paradox is that (1) an extra dollar matters much less ...
- 120k
28
votes
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27
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26
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2 Monkeys on a computer
Monkey problem
To settle down which monkey is faster on average, I'll use Markov chains and Mathematica. Define a state $i$, for $i = 0..6$, as that the monkey 1 has currently written $i$ correct ...
- 361
25
votes
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24
votes
Three horse race
It is
The following scenarios are compatible with the information given:
Scenario 1:
Scenario 2:
Scenario 3:
- 21.3k
23
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How to simulate one die with three dice?
@Deusovi's answer is totally correct, but I want to add here the general approach for solving such problems as well. No need to upvote, since I did not invent the technique, and you can see it ...
- 6,964
23
votes
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23
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What is the probability that your life will have lasted for 100 years once you die?
The frequentist answer to this question is
This is because
- 488
22
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22
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100 pieces 1 opportunity, choose wisely!
Other people have already given correct answers, but I wanted to suggest a different way of thinking about the question that involves less calculation:
- 120k
22
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frog on a number line
It's easy to see by transforming the problem into a symmetric one - instead of a 1/3 vs. 2/3 jump to B or D, make a third branch so it's a uniform 1/3 chance of going to B, D, or D' (which in turn has ...
- 4,804
21
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Monty Hall variation
A difference between the Monty Hall scenario and the train platform scenario is that
After you remember that the train will definitely not be leaving from platform 2,
- 120k
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21
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20
votes
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Only top scored, non community-wiki answers of a minimum length are eligible