Question

When 3 dice are thrown simultaneously. What is the probability that the first dice shows up a prime number, second dice shows up an odd number and third dice shows up an odd prime number?

Answer 1

Prime numbers are 2,3 and 5. All possible triplets with three dice showing prime numbers are (2,2,2),(2,,2,3),(2,2,5),(2,3,2),(2,3,3),(2,3,5),(2,5,2),(2,5,3),(2,5,5),(3,2,2),(3,2,3),(3,2,5),(3,3,2),(3,3,3),(3,3,5),(3,5,2),(3,5,3),(3,5,5),(5,2,2),(5,2,3),(5,2,5),(5,3,2),(5,3,3),(5,3,5),(5,5,2),(5,5,3),(5,5,5). These are all 27 cases each with probability 1/6^3 = 1/216. Hence, the required probability is 27/216 = 1/8.