A letter is chosen at random from the 11 letters of the word MATHEMATICS. If it is known that the letter chosen is a consonant, then the probability that it is M is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{2}{7}\)
The vowels in MATHEMATICS are A, E, A, I. The given condition leaves a reduced sample space of the consonants:
M, T, H, M, T, C, S (7 letters)
M appears twice among them:
\( \displaystyle P = \frac{2}{7} \)
Why the other options are incorrect
Option (2) \(\displaystyle\frac{2}{11}\) — Incorrect. This is the probability of M among all 11 letters, without the given condition.
Option (3) \(\displaystyle\frac{7}{11}\) — Incorrect. This is the probability that the letter is a consonant, the condition itself.
Option (4) \(\displaystyle\frac{1}{5}\) — Incorrect. This counts only the 5 different consonants M, T, H, C, S, but M and T appear twice each.