Answer to the two dice problem

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Michael Shackleford

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You showed them conditional probability without actually mentioning it. Great explanation.

NickKravitz

it's an odd question. the problem is in the ambiguity. if two dice are thrown, there are 11 combinations out of 36 that have at least 1 dice showing a 2. there is only one combination of 36 (two dice thrown) where the combination is 2x2. But if we throw one dice until we get a 2: and then throw the second dice: the probability of ending with two 2s is 1/6. However, if both dice are thrown at once: the probability of two 2s is 1/36. If we are only concerned with the probability of both dice being a two when one dice is also a two and they are both thrown at once: the probability of the two dice matching is 1/11.

the other part is in the ambiguity of whether the dice can (or cannot) be distinctly identified. If they are of different colors and we only run the "what's the probability of the yellow dice being a 2 when the blue dice is a 2?" well, since the probability of one dice is not concerned with what the other dice is: then it's 1/6.

rhueoflandorin

Unless the person throwing the dice is skilled in dice Sorry, I couldn't resist stirring the pot. Lol

matthewwerst

Unless you select a die to be 2, say, the white die, as in, "if we roll until the white die is 2". (I wasn't on the original thread)

rshinra

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