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If you roll a pair of standard dice, in how many ways can one of the dice be a "5"?...

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supersmartpants | Salutatorian

Posted September 12, 2013 at 10:33 PM via web

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If you roll a pair of standard dice, in how many ways can one of the dice be a "5"?

Whats the formula?

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llltkl | College Teacher | Valedictorian

Posted September 13, 2013 at 2:35 AM (Answer #1)

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If you roll a pair of fair dice, the number of total outcomes is 6^2, i.e. 36.

If the first die is "5", second die may be 1, 2, 3, 4, 5, or 6 = 6 different ways. Out of these ways, one has both of the dies showing up 5. This should be discarded. So, the number of ways =5.

Similarly, if the second die is "5", first die may be 1, 2, 3, 4, 5, or 6 = 6 idifferent ways. Out of these ways, one has both of the dies showing up 5. Discarding this value gives the number of ways =5.

So, the total number of ways one of the dice can be a "5" is 5+5=10.

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