Probability of Selecting 'M' or 'E' from the Word 'Mathematics'
Introduction
The question at hand is, 'What is the probability that if a letter is chosen at random from the word mathematics, it will be a letter "M" or "E"?'
Understanding the Problem
The word mathematics consists of 11 letters, but since we are interested in the probability of selecting either "M" or "E," we need to first identify all unique letters in the word. The unique letters are "m", "a", "t", "h", "e", "i", "c", "s," which comprise 8 unique letters.
Calculating the Probability
The probability of selecting a specific letter from a set of unique letters is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Total number of unique letters in "mathematics": 8
Total number of letters in the English alphabet: 26
Probability calculation:
Probability Number of unique letters / Total number of letters in the alphabet
Probability 8 / 26 0.3076923077, or approximately 31 percent.
Considering Only 'M' and 'E'
Now, if we specifically want to calculate the probability of selecting either the letter "M" or the letter "E," we can do so by considering the total number of each letter in the word mathematics.
Total number of letters in "mathematics": 11
Number of times 'M' appears: 2
Number of times 'E' appears: 1
Total number of favorable outcomes: 2 (M) 1 (E) 3
Probability calculation for 'M' or 'E':
Probability of selecting 'M' 2 / 11
Probability of selecting 'E' 1 / 11
Therefore, the probability of selecting either 'M' or 'E' is:
(2 1) / 11 3 / 11 ≈ 0.2727, or approximately 27.27 percent.
An Examination of the Word "Maths" for Comparison
Let us also briefly examine the word "maths," which has 5 unique letters: "m," "a," "t," "h," and "s."
Total number of unique letters in "maths": 5
Probability of selecting a specific letter from "maths": 1 / 5 0.20, or 20 percent.
It is worth noting that this result is more straightforward, as the total number of letters in "maths" is 5, and the probability of selecting any single letter is simply 1 / 5.
Conclusion
In summary, the probability of selecting a letter "M" or "E" from the word "mathematics" is approximately 27.27 percent. This calculation is based on the total number of occurrences of "M" and "E" in the word, rather than the total number of unique letters in the English alphabet.
For the word "maths," the probability of selecting a specific letter is 20 percent, given that the word has 5 unique letters.
Understanding these concepts is crucial in grasping the fundamentals of probability and can be applied to a variety of situations, including simple casino games where the house often has an advantage due to the correct odds.