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A well-balanced die is rolled once, what is the probability of getting a prime number?Question 4Answera.0.75b.0.50c.0.45d.0.33

Question

A well-balanced die is rolled once, what is the probability of getting a prime number?

Question 4
Answer:

  • a. 0.75
  • b. 0.50
  • c. 0.45
  • d. 0.33
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Solution

1. Break Down the Problem

To find the probability of rolling a prime number on a die, we need to:

  1. Identify the numbers on a standard die.
  2. Determine which of those numbers are prime.
  3. Calculate the probability based on the number of prime outcomes compared to the total outcomes.

2. Relevant Concepts

  • A standard die has six sides numbered from 1 to 6.
  • The prime numbers within this range are defined as numbers greater than 1 that have no divisors other than 1 and themselves.

3. Analysis and Detail

  1. The numbers on a die are: {1, 2, 3, 4, 5, 6}.
  2. The prime numbers in this set are: {2, 3, 5}.
    • Prime numbers:
      • 2 (only divisible by 1 and 2)
      • 3 (only divisible by 1 and 3)
      • 5 (only divisible by 1 and 5)
  3. Count of prime numbers: 3
  4. Total possible outcomes when rolling a die: 6

4. Verify and Summarize

The probability P P of rolling a prime number is calculated as: P=Number of prime outcomesTotal outcomes=36=0.5 P = \frac{\text{Number of prime outcomes}}{\text{Total outcomes}} = \frac{3}{6} = 0.5 Thus, the probability of getting a prime number when rolling a die is confirmed.

Final Answer

The correct answer is b. 0.50.

This problem has been solved

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