What is the probability that you roll a 5 and a 2?

Answer 1

We assume a 6 sided fair die. Now, note that the probability of rolling any number is independent of the probability of the outcome on the next role of the die. In probability terms we say the two events are independent this implies that is we look at the probability of A and the probability of B the probability of A and B is P(A)xP(B) Since we are look at the probability of a 5 and there are 6 possible outcomes, the probability of a 5 is 1/6 and a similar argument tells us the probability of a 2 is 1/6. Now, since they are independent, the probability of a 5 AND a 2 is 1/6 x 1/6=1/36 If you want to consider dice with different shapes and fewer than 6 numbers, the answer will change. I have considered only a 6 sided fair die since if one understands how this works, one can generalize to other scenarios. The commonly used die is called a cubic polyhedron. Dice come as many different polyhedra and these make for interesting probability questions.