Question

A letter is chosen from English alphabet. Find the probability of the letter being:
A) A vowel
B) A letter comes after P
C) A vowel or a consonant
D) Not a vowel

Answer 1

Hint: In this question, First, we need to calculate the number of favorable outcomes i.e. we say desirable events and then we find total number of events and after that we use basic formula of probability i.e.-
Probability of any Event(E)
P(E) = $\dfrac{{{\text{favorable outcomes}}}}{{{\text{total outcomes}}}}$

Complete step-by-step answer:
As we know, Total letter in English alphabet = 26
(a) A vowel
Number of vowels= 5
P (getting a vowel) = $\dfrac{5}{{26}}$
(b) A letter comes after P
P is 16th letter hence there will be 10 letters after P
P (getting a letter coming after P) = $\dfrac{{10}}{{26}}$=$\dfrac{{5}}{{13}}$
(c) A vowel or a consonant
Number of consonants = 21
Number of vowels = 5
P (getting a vowel or a consonant) = $\dfrac{{5 + 21}}{{26}} = 1$
(d) not a vowel
Number of vowels = 5
P (getting a vowel) = $\dfrac{5}{{26}}$
P(getting not a vowel) = 1−P (getting a vowel) = 1- $\dfrac{5}{{26}}$= $\dfrac{{21}}{{26}}$

Note- Probability is the measure of the likelihood that an event will occur in a Random Experiment. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.