Question

Find the probability that one will get $75$ marks in the question paper of $100$ marks.
a) $\dfrac{1}{{101}}$
b) $\dfrac{{75}}{{100}}$
c) $\dfrac{1}{{100}}$
d) $\dfrac{{75}}{{101}}$

Answer 1

Hint: To find the probability, first we will write the sample space $S$ for marks. Then, we will consider the event $E$ that one can get \[75\] marks. We will find the required probability by using the definition. That is, required probability $ = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$ where $n\left( E \right)$ is the number of favourable (desired) outcomes and $n\left( S \right)$ is the number of total outcomes.

Complete step-by-step solution:
In this example, it is given that the question paper is of $100$ marks. So, one can get marks between $0$and $100$. The sample space is the set of all possible outcomes. Therefore, in this example sample space for marks is $S = \left\{ {0,1,2,3,...,100} \right\}$. Therefore, $n\left( S \right) = 101$.
Now we will consider the event $E$ that one can get $75$ marks. That is, our desired outcome is $75$ and it is the one outcome out of total $101$ outcomes. Therefore, $n\left( E \right) = 1$.
Now we are going to find the probability of an event $E$ by using the definition. That is, $P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$.
$ \Rightarrow P\left( E \right) = \dfrac{1}{{101}}$
Hence, the probability that one will get $75$ marks in the question paper of $100$ marks is $\dfrac{1}{{101}}$.

Hence, option A is correct.

Note: If we have to find the probability that one will get $90$ marks in the question paper of $100$ marks then the answer will be the same. That is, probability of getting $90$ marks is also $\dfrac{1}{{101}}$ because $90$ is one outcome out of total $101$ outcomes. Surprisingly, getting $0$mark, getting $100$ marks or getting any marks between $0$and $100$ all have the same probability. That is, $\dfrac{1}{{101}}$.