Question

A single letter is selected at random from the word “PROBABILITY”. The probability that it is a vowel is:
A) ${\displaystyle \frac{8}{11}}$
B) ${\displaystyle \frac{4}{11}}$
C) ${\displaystyle \frac{2}{11}}$
D)  ${\displaystyle \frac{3}{11}}$

Answer 1

Hint: We know that the probability is the ratio of the number of favourable outcomes and the total number of possible outcomes. Here the possible outcomes will be the total number of letters in that given word. The favourable outcomes will be the number of vowels in that word.

Complete step-by-step solution:
Probability means possibility.
We know that the probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of possible outcomes.
That means,
$\text{Probability of an event to happen = }{\displaystyle \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}}$
In this problem the total number of possible outcomes will be the total number of letters in the word “PROBABILITY”, as we can select any one of the letter from this given word.
Therefore, the total number of letters in “PROBABILITY” = 11.
In this word we have four vowels, which is our favourable outcome.
Therefore, the number of vowels in “PROBABILITY” = 4.
Hence, the probability is $={\displaystyle \frac{4}{11}}$.
 Therefore, if a single letter is selected at random from the word “PROBABILITY”, the probability that it is a vowel is ${\displaystyle \frac{4}{11}}$.
Hence, option (b) is correct.

Note: We can make mistakes while we are counting the favourable cases, as the vowel ‘I’ is repeating twice. As we can select any one of them we need to count them separately. Otherwise we will get the wrong answer.