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Your Next Deal With The Devil – It’s 50/50….?

Posted by Karl Sharman under Tom (22 Responds)

I show you a shuffled deck of standard playing cards, one card at a time, no Jokers in the pack.
At any point before I run out of cards, you must say “RED!”.
If the next card I show is red (i.e. diamonds or hearts), you win.
As “dealer” I don’t have any control [...]

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A Deal with the Devil for £163m

Posted by Karl Sharman under Tom (37 Responds)

You have made a deal with the devil… You will win the lottery if you can decide the optimal position in the queue to buy the £163m Euromillions winning lottery ticket.
There are some conditions. Ain’t that always the way when making this sort of deal!
You will win, if your position in the queue is [...]

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Experimenting on Humans

Posted by Karl Sharman under Tom (22 Responds)

The subject of the experiment, whom we will refer to as “Chris” was privy to all the details of the experiment in advance, and participated willingly.
One Sunday evening, Chris went to sleep at the observation labs. In another part of the lab a fair coin-toss was conducted, yielding a result of heads or tails. Chris [...]

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Sphear of Probabilities

Posted by Karl Sharman under Tom (9 Responds)

Choose four points on the surface of a sphere. Each point is independently chosen relative to a uniform distribution on the sphere.
What is the probability that the center of the sphere lies inside the tetrahedron whose vertices are at the four points?
The reason this is titled Sphear is that it is a mix of sphere [...]

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How high

Posted by Chris under Tom (7 Responds)

Some (n) people are standing in a queue. On average, how many of them can say that they are taller than everyone ahead of them?
NB The person at the front of the queue, can say that he is taller than everyone ahead of him.

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