Six 6-sided dice are rolled. What is the probability that the number of dice showing even numbers and the number of dice showing odd numbers is equal?

Guest Nov 5, 2017

There are 6 choose 3 ways for 3 of the dice to show even numbers and 3 of them to show odd numbers. Each roll is even with probability 1/2 and odd with probability 1/2, so each arrangement of 3 odd numbers and 3 even number occurs with probability (1/2)^6. Thus, the probability that 3 dice out of 6 show even numbers is 5/16


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supermanaccz  Nov 5, 2017

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