Question

In a hostel, 60% of the students read Hindi newspapers, 40% read English newspapers and 20% read both Hindi and English newspapers. A student is selected at random. Find the probability that she reads neither Hindi nor English newspapers.
A) $\dfrac{1}{5}$
B) $\dfrac{2}{5}$
C) $\dfrac{3}{5}$
D) $\dfrac{4}{5}$

Answer 1

Hint: We will first make notation for each kind of category. Then, we will use the formula which is the application of sum of all the probabilities of an experiment is 1 always.

Complete step-by-step answer:
Let E denote English and H denotes Hindi.
We are given that 60% of students read Hindi.
Therefore, \[P\left( H \right) = \dfrac{{60}}{{100}} = 0.6\].
We were also given that 40% read English.
Therefore, \[P\left( E \right) = \dfrac{{40}}{{100}} = 0.4\].
It is also stated in the question that 20% of the students in the hostel read both English and Hindi.
So, \[P\left( {H \cap E} \right) = \dfrac{{20}}{{100}} = 0.2\]
We will first find the probability of finding a student who either reads Hindi or English.
This means that we want to find the value of $P(H \cup E)$.
We know that $P(H \cup E) = P(E) + P(H) - P(H \cap E)$
Putting in the values, we will get:-
$ \Rightarrow P(H \cup E) = 0.6 + 0.4 - 0.2 = 0.8$ …………..(1)
Since, we know that the option with a student is either she will read any newspaper or not.
Hence, the sum of the probability of her reading any newspaper and not reading any will be equal to 1.
Hence, $P(H \cup E) + P(H' \cap E') = 1$, where H’ represents students who do not read Hindi newspapers and E’ represents the students who do not read English newspapers.
Hence, we have: $P(H' \cap E') = 1 - P(H \cup E)$
Now, putting in the value from (1), we will get:-
$ \Rightarrow P(H' \cap E') = 1 - 0.8 = 0.2$
Hence, the required answer is \[0.2 = \dfrac{2}{{10}} = \dfrac{1}{5}\].

Hence, the correct option is (A).

Note: The students must notice that we directly converted the percentage into decimal for the probabilities. Let us understand the fact behind it. If we have a thing with 60% object A and 40% object B. If we randomly select an object from it, there is 60% that is 0.6 probability that you will get A and similarly 40% that is 0.4 probability that you get B.
Probability helps us in many aspects of our daily life as well. Thinking about the competition in any test or winning any game, probability is all you need to find your chances of scoring in it.