Understanding Probability: Choosing the Letter E from PERSEVERANCE and PROBABILITY

Probability is a fascinating and fundamental concept in mathematics, with wide-ranging applications in various fields including data analysis, statistics, and everyday decision-making. One common type of probability problem involves calculating the likelihood of selecting a specific letter from a word. In this article, we will explore the probability of selecting the letter E from the word PERSEVERANCE and PROBABILITY.

Probability of Selecting an E from PERSEVERANCE

PERSEVERANCE is a term that embodies determination and persistence. To understand the probability of selecting the letter E from this word, we need to break down the problem step-by-step.

Count the total number of letters in the word PERSEVERANCE.

PERSEVERANCE has 12 letters.

Count the number of times the letter E appears in the word.

In PERSEVERANCE, the letter E appears 4 times.

Now, we can calculate the probability of randomly selecting an E from PERSEVERANCE using the following formula:

[ P(E) frac{text{Number of Es}}{text{Total number of letters}} frac{4}{12} frac{1}{3} ]

Therefore, the probability of randomly choosing the letter E from the word PERSEVERANCE is (frac{1}{3}) or approximately 0.3333.

Probability of Selecting an E from PROBABILITY

Next, letrsquo;s consider the word PROBABILITY. This word, like PERSEVERANCE, can help us understand the concept of probability.

Count the total number of letters in the word PROBABILITY.

PROBABILITY has 11 letters.

Count the number of times the letter E appears in the word.

Unfortunately, the letter E does not appear in the word PROBABILITY. Therefore, the probability of randomly selecting the letter E from PROBABILITY is 0.

In mathematical terms, this can be expressed as:

[ P(E) frac{text{Number of Es}}{text{Total number of letters}} frac{0}{11} 0 ]

Visualizing Probability with a Simple Comparison

To provide further clarity on the concept of probability, letrsquo;s use a visual and relatable example. Imagine each letter in a word represents a different type of fruit in a basket. For instance:

Let the letter E represent apples.

Let the other letters represent other fruits (e.g., P - Pears, R - Strawberries, S - Oranges, V - Berries, V - Berries, A - Apples, N - Cherries, C - Lemons, E - Apples).

The word PERSEVERANCE represents a mix of fruits where 4 out of the 12 are apples.

Come time to pick a fruit randomly from this basket, the probability of picking an apple (letter E) would be:

[ P(text{apple}) frac{text{Number of apples}}{text{Total number of fruits}} frac{4}{12} frac{1}{3} ]

Conclusion

The concept of probability can be illustrated through simple examples like the ones we have seen with the words PERSEVERANCE and PROBABILITY. By breaking down the problem and counting the relevant elements, we can easily calculate the probability of selecting a specific letter from a word.

Remember:

[ P(E) frac{text{Number of Es}}{text{Total number of letters}} ] Understanding this formula can help you tackle a wide range of probability-related problems in mathematics and real life.

Whether you are analyzing data, making decisions based on chance, or simply exploring mathematical concepts, the principle of probability remains a powerful tool in your toolkit.