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
Solution
1. Break Down the Problem
To find the probability of rolling a prime number on a die, we need to:
- Identify the numbers on a standard die.
- Determine which of those numbers are prime.
- 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
- The numbers on a die are: {1, 2, 3, 4, 5, 6}.
- 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)
- Prime numbers:
- Count of prime numbers: 3
- Total possible outcomes when rolling a die: 6
4. Verify and Summarize
The probability of rolling a prime number is calculated as: Thus, the probability of getting a prime number when rolling a die is confirmed.
Final Answer
The correct answer is b. 0.50.
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