1Estimate the probability that the sum of your three rolls w

1.)Estimate the probability that the sum of your three rolls will be 5 or less if you toss a die three times? Please show all work so that I can understand it. I understand how to get the denominator, but do not understand how to get the numberator. Thank you!

Solution

Total number of outcome when 3 dice are thrown is 6x6x6=216

The ways by which 5 can occur as the sum of three faces as follows,

(2 2 1) (1 2 2) (2 1 2) (1 1 3) (3 1 1) (1 3 1) i.e there are 6 all possible outcomes by which 5 can turn up as the sum of three faces.

Hence the required probability is 6/216=1/36