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# Roll two dice. What is the probability to roll a sum of greater than 9 and/or a multiple of 6

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Roll two dice. What is the probability to roll a sum of greater than 9 and/or a multiple of 6

Guest Jun 5, 2017
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Sums  > 9  include

10  =  3 ways to do this

11 =   2 ways to do this

12  =  1 way to do this

6 ways to roll a sum > 9

Multiples of 6

6 =  5 ways to do this

12 =  1 way to do this

6 ways to roll a multiple of 6

And we have 36 possible outcomes

So,   N (sum > 9 and multiple of 6)  =      1  way  [rolling a 12 ]

And the P(sum > 9 and multiple of 6)  =  1/36

And N ( sum > 9 or multiple of 6 )  =  N(sum > 9) + N(multiple of 6)  - N(sum > 9 and multiple of 6)  =

6  + 6  -  1   =  11  ways

So  ...  P(sum > 9 or multiple of 6)  =  11/36

CPhill  Jun 5, 2017

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