Question

Assertion (A): Two dice are thrown together. The probability that the difference of the numbers on their upper faces equals 3 is \[\frac{1}{6}.\]

Reason (R): The total number of possible outcomes when two dice are rolled simultaneously is 36.

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 but Reason (R) is not a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The ordered outcomes with a difference of 3 are (1, 4), (2, 5), (3, 6), (4, 1), (5, 2) and (6, 3). Hence, \[P=\frac{6}{36}=\frac{1}{6}.\]

Step 2 – Reason: R is true. Two dice have \[6\times 6 = 36\] equally likely ordered outcomes.

Step 3 – Link: R gives the total number of outcomes, but not the number of favourable outcomes. Therefore, it alone does not explain the probability in A.