Question

Which is the probability of rolling the following sums with two number cubes?

Answer 1

The probability of rolling 7 is `6/36`
The probability of rolling 6 or 8 is `5/36` for each
The probability of rolling 5 or 9 is `4/36` for each
The probability of rolling 4 or 10 is `3/36` for each
The probability of rolling 3 or 11 is `2/ 36` for each
The probability of rolling 2 or 12 is `1/36` for each

Explanation:

In rolling two cubes with six sides there are 36 possibilities.

`6 xx 6 = 36`

For getting a 2 there is only one chance because there is only one way of getting a 2 (a one and a one), both dice must be a one. (same for a 12)

`1/6 xx 1/6 = 1/36`

For getting a three (3) there are two ways. ( 1+2 and 2+1) so the probability is `2/36 or 1/18.` ( same for 11)

For getting a four there are three ways. ( 2+2, 1+3 and 3+1) ( same for 10)

For getting a five there are four ways ( 2+3, 3+2, 4+1, 1+4) ( same for 9)

For getting a six there are five ways ( 3+3, 2+4, 4+2, 5+1, 1+5) (same for 8)

For getting a seven there are six ways ( 4+3, 3+4, 5+2, 2+5, 6+1, 1+6)
Seven has the greatest number of possibilities, and therefore the greatest probability.