Question

A die is thrown once, the probability of getting a prime number is$1/m$. The value of m is
(A) 1
(B)2
(C) 3
(D) Can’t determine

Answer 1

Hint-Whenever a dice is thrown, we can get any number from 1 to 6. Now, the probability of getting any prime number can be calculated by dividing the count of prime numbers from 1 to 6 with the total numbers on the dice that is 6.
Complete step -by-step solution -
As mentioned in the question, a die is thrown only once.
So, the numbers obtained on throwing dice are 1, 2, 3, 4, 5 and 6
Firstly, we need to know about the prime numbers.
A number is called a prime number when it has only two factors that is 1 and the number itself.
Let us calculate the number of prime numbers from 1 to 6
1 is neither a prime number nor a composite number.
2 has only 2 factors that is 1 and the number itself that is 2. So, it is a prime number.
Similarly, 3 is also a prime number.
4 is not a prime number as it has more than 2 factors that is 1, 2 and 4
5 is also a prime number.
6 is a composite number as it has more than 2 factors that is 1, 2, 3 and 6
So, the prime numbers we get in range from 1 to 6 are 2, 3 and 5
The count of prime number is 3
$\therefore {\text{The probability of getting any prime number is }}$
$ \Rightarrow {\text{(Count of Prime Number)/(Total Count) = (3)/(6)}}$
$ = 1/2$
$\therefore {\text{The value of m is 2}}$
$\therefore {\text{B is the correct option}}$

Note-In these types of questions, we should know how to calculate probability. The general form to calculate the probability of anything is to divide the count of favourable things by the total number of things.