A pair of six-sided dice is thrown. If the dice are fair, what is the probability that the dice show doubles or a sum less than 10?

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Feb 8, 2018

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#28/36=7/9#

Explanation:

The possible rolls of a pair of fair dice is:

#((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(1|,2,3,4,5,6,7),(2|,3,4,5,6,7,8),(3|,4,5,6,7,8,9),(4|,5,6,7,8,9,10),(5|,6,7,8,9,10,11),(6|,7,8,9,10,11,12))#

The number of rolls that are 10 and above is 6, which means the number of rolls that sum to less than 10 is #36-10=26#. To this, we need to add double 5 (sum 10) and double 6 (sum 12), for a total of 28 rolls that meet the conditions. This is from a possible 36 rolls, giving a probability of:

#28/36=7/9#

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