Question

If a letter is chosen at random from the letter of English alphabet, then the probability that it is a letter of the ward ‘DELHI’ is:-
A). ${}^{1}/{}_{5}$.
B). ${}^{1}/{}_{26}$.
C). ${}^{5}/{}_{26}$.
D). ${}^{21}/{}_{26}$.

Answer 1

Hint: Probability of an event is given as the ratio of favourable outcome to the total no of outcome . It is the outcome that the situation desires.

Complete step-by-step answer:
As discussed in the hint the probability is given by
$\text{probability}\ \ \text{=}\ \ \dfrac{\text{favourable}\ \text{outcome}}{\text{total}\ \text{no}\ \text{of}\ \text{outcome}}$
No favourable outcome here is that the letter selected from the English alphabet should be from the letter of the word ‘DELHI’ .
Since there are 5 letter in the world ‘DELHI’
$\therefore \ \text{favourable}\ \text{outcome}\ \text{=}\ \text{5}$
Now the total no of outcomes is the total no of ways you can select a letter from English alphabet.
Since there are 26 letters in English letter you can select them in 26 ways.
$\text{total}\ \text{no}\ \text{of}\ \text{outcome}\ \text{=}\ \text{26}$
$\therefore \ \text{probability}\ \text{=}\dfrac{\text{favourable}\ \text{outcome}}{\text{total}\ \text{no}\ \text{of}\ \text{outcome}}$
          $=\ \dfrac{5}{26}$
$\therefore \ \text{The}\ \text{probability}\ \text{is}\ \dfrac{5}{26}$

$\therefore $ The correct option is C.

Note: Suppose if the question was that the letter selected should not be from the word ‘DELHI’. Then you can simply get the answer as (1-probability that it is from the word ‘DELHI’). As sometimes it is easy to calculate the opposite of what is desired in the question.