Math Problem Statement

The table below shows the probability that a random letter on a page in a book is a vowel (A, E, I, O, or U). What is the probability that a random letter is not a vowel? Give your answer as a percentage (%).

Solution

To calculate the probability that a random letter is not a vowel, we first sum up the probabilities of all vowels provided in the table and then subtract that sum from 100%.

Step 1: Sum up the probabilities of vowels

  • Probability of A: 15%15\%
  • Probability of E: 22%22\%
  • Probability of I: 11%11\%
  • Probability of O: 6%6\%
  • Probability of U: 2%2\%

Total probability of vowels=15+22+11+6+2=56%\text{Total probability of vowels} = 15 + 22 + 11 + 6 + 2 = 56\%

Step 2: Calculate the probability of not a vowel

The probability of not being a vowel is the complement of being a vowel:

Probability of not a vowel=100%56%=44%\text{Probability of not a vowel} = 100\% - 56\% = 44\%

Final Answer:

The probability that a random letter is not a vowel is 44%.

Let me know if you need further clarification!


Here are 5 related questions for further practice:

  1. What is the probability of randomly selecting a letter that is either A or E?
  2. If the probabilities represent a single page, what is the chance of randomly picking a consonant on two consecutive pages?
  3. How would the total probability change if the probability of E was reduced to 20%?
  4. If the probabilities are based on a book with 10,000 letters, how many are expected to be vowels?
  5. How do these probabilities relate to general frequency distributions of vowels in English text?

Tip: When working with probabilities, always ensure that the total probabilities sum to 100% to verify the accuracy of your data!

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Math Problem Analysis

Mathematical Concepts

Probability
Complement Rule

Formulas

P(Not A) = 1 - P(A)
Sum of Probabilities of Events

Theorems

Complement Rule

Suitable Grade Level

Grades 6-8