Question

If a vowel is selected at random from the English alphabet then what will be the probability that it will get the vowel ‘U’?
A. \[\dfrac{7}{{12}}\]
B. \[0\]
C. \[1\]
D. \[\dfrac{1}{5}\]

Answer 1

Hint: The given problem revolves around the concept of probability. So, we will use the definition of probability for each iterations for a given number of outcomes. The probability of an event A is denoted by ‘p (A)’ and the basic formula of finding probability is\[p\left( A \right) = \dfrac{{n\left( s \right)}}{{n\left( A \right)}}\], where ‘n(s)’ denotes the favorable outcomes and ‘n (A)’ denotes the total number of outcomes for an respective event.

Complete step-by-step answer:
Since, we have given that
Here, the vowels are fair which are selected randomly, these outcomes has possibilities of getting all these vowels from the respective English alphabet that is ‘\[a\]’, ‘\[e\]’, ‘\[i\]’, ‘\[o\]’ and ‘\[u\]’ respectively.
Hence, there are a total of ‘\[5\]’ vowels in the entire alphabet series.
As a result, we know that to calculate any of the desired probability
Probability, \[p\left( A \right) = \dfrac{{n\left( s \right)}}{{n\left( A \right)}}\]
Where,
$n\left( A \right) = $Total number of outcomes of an event that is, $n\left( A \right) = 5$
$n\left( s \right) = $Individual outcome in an event, and
$p\left( A \right) = $Probability of the required outcome
Now,
Hence, to find the probability of getting the vowel ‘${\text{U}}$’ in an respective event is ‘one’ when since randomly chosen or selected at a once i.e.
$n\left( s \right) = 1$
Hence, substituting the values in the above formula, we get
\[ \Rightarrow p\left( A \right) = \dfrac{{n\left( s \right)}}{{n\left( A \right)}} = \dfrac{1}{5}\]
$ \Rightarrow $Hence, the probability of getting the vowel ‘\[{\text{U}}\]’ is \[\dfrac{1}{5}\] respectively.
So, the correct answer is “Option D”.

Note: One should know the basic formula of probability while solving a question. We should also know the concepts of independent events and that their probabilities are not affected by each other’s occurrences. Also, remember that, the sum of the probabilities of all the outcomes in the respective event is always one, so as to be sure of our final answer.