What is the probability of drawing a consonant from the letter of the word School

What is the probability of choosing a consonant from the word CONSONANT if the letters are chosen randomly? 

  1. 3/2
  2. 2/3
  3. 4/9
  4. 1/3

Answer (Detailed Solution Below)

Option 2 : 2/3

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History of Indian Constitution

15 Questions 15 Marks 9 Mins

Given-

The given word is CONSONANT

Formula Used-

Probability = [Number of successful outcomes(nE)/Total number of outcomes(nS)]

Calculation- 

Number of consonants in the word CONSONANT = 6(C, N, S, N, N, T)

Total number of letters in the word = 9(C, O, N, S, O, N, A, N, T)

∴ Probability of choosing a consonant = nE/nS

⇒ 6/9

⇒ 2/3

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A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant?

Answer

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Hint: For finding the probability of getting a consonant, we can use the equation of probability. Since probability is the number of favourable in total number, knowing the number of consonants and total number of letters in the alphabet, we can find the answer.

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

Complete step-by-step answer:
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 $26 - 5 = 21$.
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,
$P(C) = \dfrac{{21}}{{26}}$
$\therefore $ The probability that the chosen letter is consonant is $\dfrac{{21}}{{26}}$.

Note: We can also solve the problem in another way. We know the sum of probabilities 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 $\dfrac{5}{{26}}$. So the probability of getting consonant is $1 - \dfrac{5}{{26}} = \dfrac{{21}}{{26}}$.

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What is the probability of drawing a consonant from the letter of the word?

(ii) probability of choosing consonant is 117.

What is the probability of drawing a vowel from the letter of the word school?

Answer: The probability of drawing a vowel is 5/26.

What is the probability of getting a consonant?

probability is 21/26.

How many consonants are in the word probability?

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.