Question

Assertion (A): A fair die is thrown once. The probability of getting a prime number is \[\frac{1}{2}.\]

Reason (R): A natural number is prime if it has only two factors.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The prime-number faces are 2, 3 and 5, giving \[\frac{3}{6} = \frac{1}{2}.\]

Step 2 – Reason: R is true. A prime natural number has exactly two factors.

Step 3 – Link: Using the definition in R, the prime faces are 2, 3 and 5. Counting them establishes the probability stated in A.