Question

a letter of English alphabet is chosen at random . Determine the probability that the letter is a consonant.​

Answer 1

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Formula used: Probability of event is obtained by dividing the number of favourable outcomes by total number of outcomes.

Given: that a letter of English alphabet is chosen at random.

We have to find the probability that the chosen letter is a consonant.

Consonants are letters other than vowels in the alphabet.

In English alphabet we have five vowels which are “a, e, i, o & u”.

Since there are 26 letters in total, we get the number of consonants as 26−5=21.26 letters in total, we get the number of consonants as 26−5=21.

Probability of an event is obtained by dividing the number of favourable outcomes by total number of outcomes.

So here the probability of getting a consonant is found by dividing the number of consonants by the total number of letters in English alphabet.

If C is the event of getting consonant we have,C is the event of getting constant we have,

$⇒P(C) = \frac{21}{26}$

The probability that the chosen is consonant is

$= \frac{21}{26}$

we can solve the problem in another. We have the sum of probability is equal to one.

when choosing a letter from English alphabet at random, there are only two possibilities; either vowel or consonant. since there are five vowels,

The probability of getting a vowel is

$= \frac{5}{26}$

So the probability of getting consonant is

$= 1 - \frac{5}{26} = \frac{21}{26}$

$⇒ \frac{5}{26}$

So probability of getting consonant is

$= \frac{21}{26}$

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