Question

# A letter of English alphabet is chosen at random. Determine the probability that a letter does not come in the word MATHEMATICS.

We will consider the letters occurring in the word MATHEMATICS. The letters of the word are $\left\{ M,A,T,H,E,I,C,S \right\}$.The number of such letters are 8.
The number of letters not coming from the word MATHEMATICS is equal to total number of letters in English alphabets $-$ number of letters coming from word MATHEMATICS. Thus, the number of letters not coming from the word MATHEMATICS $=26-8=18$.
Thus, the probability of getting a letter which doesn’t occur in word MATHEMATICS $=\dfrac{18}{26}=\dfrac{9}{13}$.
Hence, the probability that a letter does not come in the word MATHEMATICS is $\dfrac{9}{13}$.
Note: Probability of any event describes how likely an event is to occur or how likely it is that a proposition is true. The value of probability of any event always lies in the range $\left[ 0,1 \right]$ where having 0 probability indicates that the event is impossible to happen, while having probability equal to 1 indicates that the event will surely happen. We must remember that the sum of probability of occurrence of some event and probability of non-occurrence of the same event is always 1.