Question

If a die is thrown once, then the probability of getting a prime number is

• A. \(\frac{1}{6}\)
• B. \(\frac{1}{3}\)
• C. \(\frac{2}{3}\)
• D. \(\frac{1}{2}\)

Answer 1

The Correct Option is D

Step 1: List all possible outcomes.

A standard die has six faces, numbered \(1, 2, 3, 4, 5, 6\). Thus, the total number of outcomes is 6.

Step 2: Identify the prime numbers among the outcomes.

A prime number is a number greater than 1 that has no divisors other than 1 and itself. Among the numbers \(1, 2, 3, 4, 5, 6\), the prime numbers are:

\[ 2, 3, 5. \]

There are 3 prime numbers.

Step 3: Compute the probability.

The probability is the ratio of favorable outcomes (prime numbers) to total outcomes:

\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6}. \]

Simplify:

\[ \text{Probability} = \frac{1}{2}. \]

Final Answer: The probability of getting a prime number is \( \mathbf{\frac{1}{2}} \), which corresponds to option \( \mathbf{(4)} \).