Question

What is the probability of selecting “W” from the letters of the word SWORD?
A. $1$
B. $0$
C. $\dfrac{1}{5}$
D.$\dfrac{2}{5}$

Answer 1

Hint: The given query is based on the formula of probability that the word should be provided and we discover the occurrence of one letter. Probabilities can be expressed as proportions based on the total word and defined as the one letter to be determined from the given word.

Useful formula:
Probability is measured as a number between $0$ and $1$, where $0$ indicates impossibility and $1$ indicates certainty.
Probability formula,
Given by,
$p\left( A \right) = \dfrac{{{\text{Number}}\,{\text{of}}\,{\text{favorable}}\,\,{\text{events}}}}{{{\text{Number}}\,{\text{of}}\,{\text{total}}\,{\text{events}}}}$
Probability of $A$, $p\left( A \right) = \dfrac{{n\left( A \right)}}{n}$
Probability of $B$, $p\left( B \right) = \dfrac{{n\left( B \right)}}{n}$
Where, $n$ is the number of total events
$n\left( A \right)$ and $n\left( B \right)$is the number of favorable events

Complete step-by-step answer:
Using the given probability formula,
\[{\text{probability = }}\dfrac{{{\text{favorable}}\,{\text{outcome}}}}{{{\text{total}}{\text{.no}}\,{\text{outcome}}}}\]
The probability of the “W” from the letters of the word SWORD
${\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes = 5}}$
The W comes in $1$ time in SWORD and there are total $5$letters
${\text{Favorable}}\,{\text{outcomes = 1}}$(W)
By a given probability formula,
Substituting a above value in the given probability formula,
We get,
Probability $ = \dfrac{1}{5}$
Hence the above given option C is the answer probability $p\left( A \right) = \dfrac{1}{5}$.

Note: Whenever we are uncertain about the outcome of an occurrence in this above problem, we take the probabilities of such results to evaluate the given term. It is similar to the basic idea of permutation and combination to define a letter from the given word and the information to determine a probability function in a number of ways.