Question

In a city, $20\% $ people read English newspapers, $40\% $ read Hindi newspapers and $5\% $ read both newspapers. The percentage of non-reader either paper is
A. $60\% $
B. $35\% $
C. $25\% $
D. $45\% $

Answer 1

Hint: In this question we have to find the percentage of non-reader either paper which means that we have to find the probability of persons who do not read both papers. We will first try to write the given percentage numbers in simpler forms and then we will apply the formula.

Formula used:
$P(E' \cap H') = 1 - P(E \cup H)$

Complete step-by-step answer:
Here we have been given that the probability of people who read English newspapers:
$P(E) = 20\% $
We can write this value in simplified from as:
 $ \Rightarrow \dfrac{{20}}{{100}} = \dfrac{1}{5}$
The probability of people who read Hindi newspapers are:
$P(H) = 40\% $
Again we can write the value in simpler terms as:
$ \Rightarrow \dfrac{{40}}{{100}} = \dfrac{2}{5}$
Now we have the probability of people who read both English and Hindi newspapers i.e. $P(E \cap H) = 5\% $ .
It can also be written as
 $ \Rightarrow \dfrac{5}{{100}} = \dfrac{1}{{20}}$ .
We need to find $P(E' \cap H')$
From the formula we have
$P(E' \cap H') = 1 - P(E \cup H)$
We can further simplify
$ \Rightarrow P(E \cup H) = P(E) + P(H) - P(E \cap H)$
By substituting this value back in the formula we can write:
 $ \Rightarrow P(E' \cap H') = 1 - \left( {P(E) + P(H) - P(E \cap H)} \right)$
We will now substitute the values from above and we have:
$ = 1 - \left( {\dfrac{1}{5} + \dfrac{2}{5} - \dfrac{1}{{20}}} \right)$
On simplifying it gives:
$ \Rightarrow 1 - \left( {\dfrac{{4 + 8 - 1}}{{20}}} \right) = 1 - \dfrac{{11}}{{20}}$
It gives us value:
 $ \Rightarrow \dfrac{{20 - 11}}{{20}} = \dfrac{9}{{20}}$ .
Therefore it gives us
$ \Rightarrow P(E' \cup H') = \dfrac{9}{{20}}$
We have to convert the value in percentage so we will multiply the above fraction with $100$:
$ = \dfrac{9}{{20}} \times 100$
It gives us value in percentage $45\% $
Hence the correct option is (d) $45\% $ .

So, the correct answer is “Option (d)”.

Note: We should always remember the formulas before solving this kind of question. We should know that probability means possibility. So we can say that probability theory is the branch of mathematics that deals with the possibility of the happening of events. By depending on the type of probability we apply the formula and solve it.