Math Problem Statement

Which of the following values could be a probability? √(1/2), 2, 11/3, 0.2523, or √5.

Solution

To determine which values could be a probability, we need to remember that probabilities are always between 0 and 1, inclusive. Any value outside this range is not a valid probability.

Now, let's evaluate each of the options in the image:

  1. 12\sqrt{\frac{1}{2}}: The square root of 12\frac{1}{2} is approximately 0.707, which lies between 0 and 1, so this could be a probability.

  2. 2: This is greater than 1, so it cannot be a probability.

  3. 113\frac{11}{3}: The value of 113\frac{11}{3} is approximately 3.67, which is greater than 1, so it cannot be a probability.

  4. 0.2523: This value is between 0 and 1, so it could be a probability.

  5. 5\sqrt{5}: The square root of 5 is approximately 2.236, which is greater than 1, so it cannot be a probability.

Conclusion:

The values that could be a probability are:

  • 12\sqrt{\frac{1}{2}}
  • 0.2523

Would you like further details or explanations on any of these values?

Here are 5 related questions for further exploration:

  1. What is the definition of a valid probability distribution?
  2. Can probabilities ever be negative? Why or why not?
  3. What are some real-world examples of probabilities?
  4. How is probability used in statistics and data analysis?
  5. How do you calculate probabilities for independent events?

Tip: Always remember that probabilities are values between 0 and 1, inclusive. Anything outside this range is invalid in a probability context.

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Math Problem Analysis

Mathematical Concepts

Probability
Square Roots
Fractions
Decimals

Formulas

Probability Range: 0 ≤ P ≤ 1

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 7-9