# Probability of dice questions

In this chapter we will solve questions related to calculating probability by rolling a dice.

We know that in a dice, we have 6 numbers (1 to 6), so the sample size for the experiment is expressed as;
S = { 1, 2, 3, 4, 5, 6 }

Hence, there are 6 possible outcomes after rolling a dice.

I hope you understood the basics, let us solve some problems, related to the concept.

## Dice Probability – Solved examples

Example 01
In an experiment a dice is rolled. Calculate the probability of getting 2 or 4.

Solution
Let A be the event of getting 2 or 4.
A = {2, 4}

So there are 2 possible outcomes.

Probability (A) = 2/6 = 1/3

Hence, 1/3 is the required probability.

Example 02
A dice is thrown, calculate the probability of getting an odd number.

Solution
Let A be the event of getting an odd number.

A = {1, 3, 5 }
Total possible outcome = 3

Probability (A) = 3/6 = 1/2

Hence, 1/2 is the required probability.

Example 03
In an experiment a dice is rolled. If we get even number then a coin will be tossed. Calculate the probability of getting (2, Head) as possible outcome.

Solution
Let us first write the all possible outcome of the experiment.

S = { 1, 3, 5, (2,H), (2,T), (4,H), (4,T), (6,H), (6,T) }
There are 9 total outcome possible.

Let A be the event of getting (2, H)
Number of favorable outcome = 1

Probability (A) = 1/9

Hence, 1/9 is the required probability.

Example 04
Consider the experiment of rolling a dice. If the outcome is odd number then another dice will be thrown. Calculate the probability of getting same number on both dice.

Solution
Writing the sample space for given experiment.

S = { 2, 4, 6, (1,1), (1,2), (1, 3), (1, 4), (1, 5), (1, 6)
(3,1), (3,2), (3, 3), (3, 4), (3, 5), (3, 6)
(5,1), (5,2), (5, 3), (5, 4), (5, 5), (5,6) }

Total possible outcomes = 21

Let A be the event of getting same number on both dice.

A = {(1,1), (3, 3), (5,5)}
Total favorable outcome = 3

Probability (A) = 3/21

Hence, 3/21 is the required probability.