A letter of english alphabets is chosen at random.What is the probability that it is a letter of the word MATHEMATICS.
First find out how many distinct letters are there in the word MATHEMATICS, call this number "n".
For example, the word SAILING has the letters S,A,I,L,N,G, 6 out of 7 letters are distinct, while the letter I is repeated but not counted more than once.
In the English alphabet, there are 26 distinct letters.
Assuming that the probability is equal for choosing any one of the 26 letters, then the probability of choosing any one letter out of the word MATHEMATICS is n out of 26, or
n/26, where n has been counted in the first paragraph.
MATHEMATICS=8/26 OR 11/26
To find the probability that a randomly chosen letter is a letter of the word "MATHEMATICS," we need to determine the total number of letters in the word and divide it by the total number of letters in the English alphabet.
Step 1: Count the total number of letters in the word "MATHEMATICS."
The word "MATHEMATICS" contains 11 letters.
Step 2: Count the total number of letters in the English alphabet.
The English alphabet contains 26 letters.
Step 3: Calculate the probability.
The probability is given by the formula:
Probability = Number of desired outcomes / Total number of possible outcomes
In this case, the desired outcome is choosing a letter from the word "MATHEMATICS," which is 11. The total number of possible outcomes is the total number of letters in the English alphabet, which is 26.
Probability = 11 / 26
Simplifying the fraction gives:
Probability = 0.423
Therefore, the probability that a randomly chosen letter is a letter of the word "MATHEMATICS" is approximately 0.423, or 42.3%.
To find the probability that the chosen letter is a letter of the word MATHEMATICS, we need to determine the total number of letters in the word and the total number of letters in the English alphabet.
Total number of letters in the word MATHEMATICS = 11 (including repetitions of letters)
Total number of letters in the English alphabet = 26
Since the word MATHEMATICS has repetitions of letters, we need to count each letter only once. Referring to the word, we have the letters M, A, T, H, E, I, C, S. So, the total number of unique letters in the word is 8.
Therefore, the probability that the chosen letter is a letter of the word MATHEMATICS is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Number of favorable outcomes = 8 (number of unique letters in the word MATHEMATICS)
Total number of possible outcomes = 26 (total number of letters in the English alphabet)
Probability = 8/26 = 4/13
Thus, the probability that the chosen letter is a letter of the word MATHEMATICS is 4/13.