Question

Imagine rolling two fair 6 sided dice. What is the probability the number rolled on the first die is even or the sum of the rolls is 10?

Answer #1

Here are the possibities of rolling two fair 6 sided dice.

Here there are total of 6 * 6 = 36 possiblities.

these are the possibilities.

sum is 2 = (1,1)

sum is 3 = (1,2), (2,1)

sum is 4 = (1,3), (3,1), (2,2)

sum is 5 = (1,4), (4,1), (2,3), (3,2)

sum is 6 = (1,5), (5,1), (2,4), (4,2), (3,3)

sum is 7 = (1,6), (2,5), (3,4),(4,3), (5,2), (6,1)

sum is 8 = (2,6), (3, 5), (4,4), (5,3), (6,2)

sum is 9 = (3,6), (4,5), (5,4), (6,3)

sum is 10 = (4,6), (5,5), (6,4)

sum is 11 = (5,6), (6,5)

sum is 12 = (6,6)

Here first die is even so here there are 18 possibliites.

here total possiblities when the sum of the rolls is 10 = 3

so here common possibliies where first die is even and the sum of the rolls is 10 are 2 [(4,6) and (6,4)]

so here total possiblities = 18 + 3 -2 = 19

so probability that number rolled on the first die is even or the sum of the rolls is 10 = 19/36

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