Probability of Selecting A or T from the Word ‘Mathematics’: An SEO-Optimized Guide

When dealing with probability, one common scenario is to calculate the likelihood of selecting specific letters from a given word. In this article, we will explore how to determine the probability of randomly picking the letters A or T from the word mathematics. By following a step-by-step approach, this guide will help you understand the underlying concepts and accurately compute the desired probability.

Step-by-Step Probability Calculation

To find the probability of randomly selecting the letters A or T from the word mathematics, we need to consider the total number of letters and the number of favorable outcomes. Here’s how to proceed:

Total Number of Letters

First, we count the total number of letters in the word mathematics. The word mathematics consists of 11 letters.

Occurrences of A and T

Next, we count the occurrences of the letters A and T within the word mathematics: The letter A appears 2 times. The letter T appears 2 times.

Total Occurrences of A or T

To find the total number of favorable outcomes (selecting either A or T), we add the occurrences of A and T. Thus, the total occurrences of A or T is 2 2 4.

Calculate the Probability

The probability of selecting A or T can be calculated using the formula:

P(A or T) number of favorable outcomes / total number of outcomes

Substituting the values we have:

P(A or T) 4 / 11

Therefore, the probability of randomly selecting the letters A or T from the word mathematics is 4/11.

Using Set Theory to Confirm the Probability

Using set theory, we can also confirm the probability of selecting A or T. Let’s break it down:

Union of Sets

In set theory, the probability of choosing an element from the union of two sets (in this case, choosing A or T) can be calculated as:

P(A or T) P(A) P(T) - P(A and T)

Since A and T are mutually exclusive in this context (you can't choose the same letter twice), P(A and T) 0. Hence, the equation simplifies to:

P(A or T) P(A) P(T)

We know that:

P(A) 2/11 (since there are 2 As out of 11 letters) P(T) 2/11 (since there are 2 Ts out of 11 letters)

Therefore:

P(A or T) 2/11 2/11 4/11

Conclusion

The probability of randomly selecting the letters A or T from the word mathematics is 4/11. This method not only confirms the initial calculation but also provides a deeper understanding of the underlying mathematical principles.