Probability of Selecting a Letter from the Word 'Mathematics'
Introduction
When dealing with the English alphabet and specific words, one can explore a myriad of probability questions. A classic example is determining the probability of selecting a letter at random from the word 'Mathematics.' This article aims to address this inquiry step-by-step, providing clarity and supporting the answer with a well-explained solution.
Understanding the Problem
The question asks for the probability of selecting a letter from the word 'Mathematics' when a letter is chosen at random from the entire English alphabet. This implies that we need to find the likelihood of picking one of the letters in the word 'Mathematics' from a set of 26 letters.
Identifying Unique Letters
The first step in solving this problem is to identify the unique letters in the word 'Mathematics.' The letters in 'Mathematics' are:
M A T H E I C SThese are the unique letters and there are a total of 8 unique letters.
Total Number of Letters in the English Alphabet
The English alphabet consists of 26 letters. This forms the total number of possible outcomes when selecting a letter at random from the alphabet.
Calculate the Probability
The probability of selecting a letter from the word 'Mathematics' can be determined using the following formula:
Pmathematics Number of favorable outcomes / Total number of outcomes
Here, the number of favorable outcomes is the number of unique letters in 'Mathematics' (8), and the total number of outcomes is the total number of letters in the English alphabet (26).
Find the Fraction
Pmathematics 8 / 26
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
Pmathematics 4 / 13
Conclusion
The probability of selecting a letter from the word 'Mathematics' when a letter is chosen at random from the English alphabet is 4/13, or approximately 30.77%.
Additional Analysis
To further understand the concept, let's consider an analogy with a similar but simplified scenario:
Imagine selecting a letter randomly from the word 'Maths.' The word 'Maths' contains 5 unique letters. Therefore, the probability of selecting one of these 5 letters is:
PMATHS 5 / 26 ≈ 0.1923 or 19.23%.
This is less than the probability for 'Mathematics,' as 'Mathematics' has more unique letters.
Real-World Application
The concept of probability in such scenarios is not as abstract as it might seem. For example, in the context of gambling, the odds mentioned (such as three to one for a winning bet) are often used to ensure the casino has a favorable advantage, which is the house edge in the long term.