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5 dice of the standard 6 sided dice, whats the probability of getting a pair?

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  • 5 dice of the standard 6 sided dice, whats the probability of getting a pair?


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Answer #1 | 18/12 2013 00:19
It's easiest to figure out how NOT to get a pair, then just subtract from 1.00. First dice - no chance. Second dice - 5/6 chance to NOT get a pair. Third dice 4/6 (or 2/3) chance to NOT get a pair. Fourth dice 1/2 chance. Fifth dice 1/3 chance. Probability of NOT getting a pair = 5/6 * 2/3 * 1/2 * 1/3 = 10/108 or 5/54. As a decimal number, that's approximately 0.0926. Now to figure out the chance you will get at least 1 pair, subtract that number from 1.00. 1.00 = 0.0926 = 0.9074. That's your answer. The probability is 0.9074, or 90.74%. 90.74% means that more often than 9/10 times you roll 5 six-sided dice, you will get at least 1 pair.

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