Explanation Three cases arise:
Case 1: When only one dice shows up a six
This dice can be any of the 1st, 2nd or 3rd dice. Find the probability for these three independent events and add them up to get the total probability
Probability that only 1st dice shows up a six: (probability that first dice shows up a 6) and (probability that second dice shows up other than 6) and (probability that third dice shows up other than 6)
=(1/6)*(5/6)*(5/6)
=25/216
similarly probability that 2nd dice shows up a six: (5/6)*(1/6)*(5/6) = 25/216
And, probability that 3rd dice shows up a six: (5/6)*(5/6)*(1/6) = 25/216
So probability that only one dice shows up a six: (25/216)+(25/216) +(25/216) = 75/216
Case 2:When two dice show up a six
Total number of ways of selecting a pair of dice that show up a six from a set of 3 dice are: 3C2=3
Find the probability of getting six on a pair of dice and multiply it by total number of such possible pairs
Probability of getting a six on a pair of dice = (1/6)*(1/6)*(5/6) = 5/216
So, total probability = 3*(5/216) = 15/216
Case 3: When all dice show up a six
In this case total probability is just (1/6)*(1/6)*(1/6) = 1/216
So total probability of getting at least one six = (75/216) + (15/216) + (1/216) = 91/216