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

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Hint: Consider all the letters occurring in the word MATHEMATICS. Find all the letters which don’t occur in this word. Count the number of such letters. Use the formula of probability which is equal to the ratio of number of favourable events to the total number of events, to calculate the given probability.

Complete step-by-step answer:

We have the word MATHEMATICS. We have to calculate the probability of choosing a letter that 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 \[=26-8=18\].

We know that probability of any event is the ratio of the number of favourable outcomes to the total number of possible outcomes.

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.

Complete step-by-step answer:

We have the word MATHEMATICS. We have to calculate the probability of choosing a letter that 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 \[=26-8=18\].

We know that probability of any event is the ratio of the number of favourable outcomes to the total number of possible outcomes.

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.

Last updated date: 20th Sep 2023

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