Question

An unbiased die is thrown. What is the probability of getting:
(1) an even number and (2) a multiple of 3.

Answer 1

Hint: This question is simply based on the definition of probability. Here we will first find the favourable events and then use a formula for finding the probability. In such a type of question where an occurrence of one event is a subset of the other event.

Complete step-by-step solution -
In the question it is given that an unbiased coin is thrown and we have to find the probability of getting an even number in the first part and a multiple of 3 in the second part.
Sample space when a dice is thrown is $\left\{1,2,3,4,5,6\right\}$
$\therefore$ On throwing a dice total possible events =6
(1)
Here the favourable event is the occurrence of an even number.
Sample space of favourable event is $\left\{2,4,6\right\}$
So total number of favourable events = 3.
Now, we know that the formula for finding probability is given as:
Probability = ${\displaystyle \frac{\text{Total number of favourable events}}{\text{Total number of possible events}}}$ .
Putting the values in above formula, we get:
Probability = ${\displaystyle \frac{3}{6}}={\displaystyle \frac{1}{2}}$
(2)
Here the favourable event is the occurrence of a multiple of 3.
Sample space of favourable event is $\left\{3,6\right\}$ .
So total number of favourable events = 2

Now, we know that the formula for finding probability is given as:
Probability = ${\displaystyle \frac{\text{Total number of favourable events}}{\text{Total number of possible events}}}$ .
Putting the values in above formula, we get:
Probability = ${\displaystyle \frac{2}{6}}={\displaystyle \frac{1}{3}}$ .

Note: Before solving this type of question you should remember the formula for finding the probability. Here a dice is thrown. You should know that on throwing a dice the total number of possible events is equal to 6. And depending on what is given is a question you have to calculate the number of favourable events and then use the formula for finding the probability.