Two of my students, Dumber and Dumberer play a game based on the total roll of two standard dice. Dumber posits that a 12 will be rolled first. Dumberer says that two consecutive 7s will be rolled first.

They keep rolling until one of them wins. What is the probability that Dumber will win?

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Probabilities
This question was asked today, and the first person I thought of was Chris. I have no answer yet, and the fact that probabilities come into it, means I never will….

A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up [...]

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Probabilities
Twenty-seven identical white cubes are assembled into a single cube, the outside of which is painted black. The cube is then disassembled and the smaller cubes thoroughly shuffled in a bag. A blindfolded man (who cannot feel the paint) reassembles the pieces into a cube. What is the probability that the outside of this cube [...]

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Maths,

Probabilities
An urn contains a number of coloured balls, with equal numbers of each color. Adding 20 balls of a new color to the urn would not change the probability of drawing (without replacement) two balls of the same color.

How many balls are in the urn? (Before the extra balls are added.)

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Probabilities
Baron von Richthofen died on this day in 1918 – He was a fighter Ace in WW1 – so, on that tenuous link, here’s an Ace question by Martin Gardner 1914-2010 – After going down in flames for my last question, this is a probability question by someone else…

Someone deals you a bridge hand (13 [...]

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Probabilities
Following on from Chris’s questions on probabilities in a deck of cards…. and I really hope I have the right answer or Chris will never let me hear the end of this…

You have a deck of cards which you thoroughly shuffle. Next, you start to deal them, face-up, counting the cards as you go. “One, [...]

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Probabilities
You are lost in the woods. You come to a T-junction and are wondering which way to go. You have a funny feeling that one way will get you out, the other will mean certain death. Weird, eh?

Wizard of Oz approaches you. “A left turn will get you out of the woods,” he advises. [...]

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Probabilities