Rolling Dice

In this section, we'll go over several problems involving dice rolling. This is an extremely common topic/scenario in probability, and these sorts of problems are useful to visualize.

Rolling Dice

We will go over several problems involving dice rolling.

Exercise 1

One dice is rolled. What is the probability of getting an even number?


We need to first find the number of even numbers on a dice. There are 3 even numbers, namely 2,4,6. There are 6 total numbers. Thus, the ratio of even numbers to total numbers is 1/2, and consequently, there must be a 1/2 probability of getting an even number.

Exercise 2

A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.


First, we'll find the probability o getting an odd number, and find the probability of getting heads. And then we'll use the probability operation that corresponds to "and". We can realize that these are two independent events, so the probability of both of them happening will simply be the probability of each of them happening, multiplied by each other. Can you do the rest on your own?

Hint: the answer is 1/4. Why?

Exercise 3

Two dice are thrown, what is the probability that both the die have a different number.


First, we need to realize that no matter what the first number is, the probability will always be the same. Why? Let's think about this using an example. If you roll a 5, you have 5 options on the next roll to not get a 5. If you roll a 4, you have 5 options on the next roll to not get a 5. We can notice that no matter what we roll, there will always be 5 options on the next roll to get a different number. Therefore, the probability of getting a different number will always be 5/6.

You Try It!

1. 3 Dice are thrown. What is the probability that none of the dice roll on prime numbers?

2. Find the probability of throwing a total of 8 in a single throw with two dice.

3. 2 Dice are rolled. Find the probability that the sum is greater than 5