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

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

Final Answer

The correct answer is b. 0.50.