Summing the rolls of 2 fair dice, what's the probability of rolling a prime number (so rolling a 3 and a 3 doesn't work because 6 is composite)?

1 Answer

#15/36=5/12#

Explanation:

Let's look at the problem this way - what are the possible rolls with 2 fair, standard dice. I'll highlight the prime numbers in red:

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

Of the 36 possible rolls, 15 are prime, which gives us #15/36=5/12#