Two letters are chosen one after another without replacement from the English alphabet. What is the probability that the second letter chosen is a vowel?a)4/25b)5/26c)5/25d)1/5,1/26Correct answer is option 'B'. Can you explain this answer?

Question

Answer

To find the probability that the second letter chosen is a vowel, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Number of Favorable Outcomes:
There are 5 vowels in the English alphabet: A, E, I, O, U. Since the first letter has already been chosen, there are only 4 vowels remaining for the second letter.

Number of Possible Outcomes:
Since two letters are chosen one after another without replacement, the total number of possible outcomes will decrease with each selection. The first letter can be any of the 26 letters in the English alphabet. Once the first letter has been chosen, there are 25 letters remaining for the second letter.

Therefore, the number of possible outcomes is 26 * 25.

Probability Calculation:
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes.

In this case, the probability that the second letter chosen is a vowel is given by:

Probability = Number of Favorable Outcomes / Number of Possible Outcomes

Probability = 4 / (26 * 25)

Simplifying the expression, we get:

Probability = 4 / 650

Further simplifying, we have:

Probability = 1 / 162.5

Since the probability is usually expressed as a fraction or a decimal, it is best to simplify it further. Dividing both the numerator and denominator by 2, we get:

Probability = 1/2 / 162.5 / 2

Probability = 1/325

Therefore, the correct answer is option B) 5/26.

Answer

Note : There are 21 cosonants and 5 vowels in 26 letters of alphabet.

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