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NDA 2025 Maths · Mathematics · Probability · medium

A letter is chosen at random from the letters of the word MATHEMATICS. The probability that it is a vowel is

Single correct option

A letter is chosen at random from the letters of the word MATHEMATICS. The probability that it is a vowel is
  1. A. 411\dfrac4{11}
  2. B. 311\dfrac3{11}
  3. C. 511\dfrac5{11}
  4. D. 12\dfrac12
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Answer: (A) 411\dfrac4{11}

The word has 1111 letters: M, A, T, H, E, M, A, T, I, C, S. The vowels are A, E, A, I, i.e. 44 letters counted with repetition. So P=411P=\frac4{11}. The option 311\frac3{11} counts distinct vowels A, E, I, forgetting the repeated A.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake