Question

Each letter of the word ‘INDEPENDENT’ is written on individual cards. The cards are placed in a box and mingled thoroughly. A card with letter ‘N’ is removed from the box. Now find the probability of picking a card with a constant?
A.$\dfrac{7}{{11}}$
B.$\dfrac{7}{{10}}$
C.$\dfrac{3}{5}$
D.$\dfrac{2}{5}$

Answer 1

Hint: Here in this question, we deal with probability. In order to solve probability related questions, we first need to understand what is probability and some of its related terms such as random experiment, outcome, sample space, equally likely outcomes and event. There are three different types of probability:
1.Theoretical Probability
2.Experimental Probability
3.Axiomatic Probability

Complete step by step solution:
Probability helps us to know how often an event is likely to happen.
A random experiment is a trial or an experiment whose outcomes cannot be predicted with surety or certainty. Outcome is the result of any random experiment conducted. Sample space is a set of all the possible outcomes for a random experiment. Event is a set of possible outcomes under a specified condition.
The formula of probability is the ratio of number of favorable outcomes to total number of events in the sample space.
$P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$
Where,$P\left( A \right)$ depicts the probability of an event ‘E’,$n\left( E \right)$ depicts the number of favorable outcomes and $n\left( S \right)$ depicts the total number of events in the sample space.
Now, according to the question
The total number of letters or alphabets in the word ‘INDEPENDENT’ is $11$.
From those $11$ letters, there are $4$ vowels and the rest $\left( {11 - 4} \right) = 7$ are constants.
We are given that ‘N’ which is a constant is removed. So, the remaining constants are $\left( {7 - 1} \right) = 6$.
The total number of letters left now are $\left( {11 - 1} \right) = 10$
Now, using the probability formula:
$P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$
$P\left( E \right) = \dfrac{6}{{10}} = \dfrac{3}{5}$
Hence, the required probability is $\dfrac{3}{5}$.

Therefore, option (C) is correct.

Note:
For solving such types of questions, the concept of probability and related terms should be clear. The formula for calculating probability is very easy to remember and use if the concepts are crystal clear. Probability helps to predict future events and the events which take place accordingly.