Question

If a die rolled once, then find the probability of getting an odd prime number.

Answer 1

Hint: In this question it is given that if a die rolled once, then we have to find the probability of getting an odd prime number. So for this we need to know the expression of probability, which is,
Probability(P)=$$\dfrac{\text{Number of favourable outcomes} }{\text{Total number of outcomes} }$$.....(1)
So from the given data we have to find the all possible outcomes and the number of possible outcomes.

Complete step-by-step solution:
As we know that a die is a six-sided cube with the numbers 1-6 placed on the faces.
So from here we can say that if we throw a die then among these six faces one face must occur.
Therefore, Total number of possible outcomes = 6
Now the favourable outcome is to get an odd prime number, so between 1 to 6 the odd primes are 3 and 5, i.e, only two.
So the number of favourable outcomes =2
Therefore, we can say that,
$$\text{Probability} \left( P\right) =\dfrac{\text{Number of favourable outcomes} }{\text{Total number of possible outcomes} }$$
$$=\dfrac{2}{6}$$
$$=\dfrac{1}{3}$$
So we can say that the probability of getting an odd prime number is $$\dfrac{1}{3}$$.

Note: To solve this type of question you need to know that in mathematics, prime numbers are whole numbers which are greater than 1, that have only two factors, 1 and the number itself and they are divisible only by the number 1 or itself.
For example: 2, 3, 5, 7 and 11 are the first few prime numbers.
Also you need to have the basic idea about odd numbers, so odd numbers are those numbers which are not divisible by 2 or we can say that when divided by 2, leave a remainder 1.
For example: 1, 3, 5, 7, …...