Assume that I had two tetrahedral dice four faces with value

Assume that I had two tetrahedral dice (four faces with values 2, 3, 5, and 8) and one hexahedral die (six faces with values 1, 3, 5, 7, 8 and 9). What is the size of the sample space (all different outcomes)? What is the probability of getting all three values on the three dice the same? What combination on the three dice add up to 14? What is the probability of getting the sum on the three dice of 14?

Solution

Sample size =96

Probability of getting all 3 values on the 3 dice=3/96 i.e., 3 chances are {(3,3,3),(5,5,5),(8,8,8)}.

Combination on the three dice add up to 14 is {(2,3,9),(2,5,7),(3,2,9),(3,3,8),(3,8,3),(5,2,7),(8,3,3),(8,5,1)}=8 chances

Probability of getting the sum on the three dice of 14 =8/96.