Question

A letter is chosen at random from letters of the word PROBABILITY. Find the probability that letter chosen is
$(1) $ a vowel.
$(2) $ a consonant.

Answer 1

Hint: In the above given question, count the total number of vowels and consonants in the given word. Also count the total number of letters in the same word. Using these two, we can obtain the probability of choosing a vowel or the probability of choosing a consonant.

Complete step-by-step answer:
We have the given word as PROBABILITY.
Here, the total number of letters are 11 out of which 4 are the vowels and 7 are the consonants.
Let P be the probability of choosing a vowel and P’ be the probability of choosing a consonant.
$(1)$ Since, we know that the total letters in the word PROBABILITY are 11.
The number of vowels =4
Therefore, the probability of choosing a vowel (P)$ = \dfrac{4}{{11}}$.
$(2)$ Since, we know that the total letters in the word PROBABILITY are 11.
The number of consonants =7
Therefore, the probability of choosing a consonant (P’)$ = \dfrac{7}{{11}}$.
Hence, the probability of choosing a vowel is$\dfrac{4}{{11}}$and the probability of choosing a consonant is$\dfrac{7}{{11}}$.

Note: Here, in this question, we have assumed the probability of choosing a vowel to be P, whereas the probability of choosing a consonant to be P’. After calculating P, P’ can also be obtained by subtracting the value of P from 1, that is, P’=1-P, where 1 is the total probability of the event of choosing a letter from the given word.