If two dice are rolled one time a sum of 7 11SolutionA sum

If two dice are rolled one time.
a sum of 7 & 11

Solution

A sum of 7 can be obtained as follows:

1+6, 6+1
2+5, 5+2
3+4, 4+3

The total probability to get sum of 7 is
(# of possible outcomes desired) / (# of possible total outcomes).

The # of possible outcomes desired, listed above, is 6.
The # of total outcomes is 36.
Thus the probability to get 7 is 6/36=1/6.

If the sum is 11, it could be obtained only if one dice rolls 6 and another one 5 or viceversa. There are no other possibilities.

The # of possible outcomes desired is 2.
The # of total outcomes is 36.
Thus the probability to get 11 is 2/36=1/18.