Suppose three fair dice are rolled at the same time.
a) What is the probability that at least one number will be less than 5?
b) What is the probability that the sum of the two numbers on the first and second dice will exceed the number on the third die?
c) What is the probability that the three numbers will be consecutive when sorted in increasing order? For example, (1,2,3) and (3,1,2) can both be viewed as being consecutive after sorting.
d) Given that the three numbers are consecutive (after sorting), what is the probability that there will be exactly two prime numbers? (1 is not a prime number!)