Question

suppose you roll 2 dice. what is the probability that the sum of the 2 dice is exactly 8, given that the 1st dice is a 2? express your answer as a reduced fraction.

Explanation:

Step1: Determine the condition

The first - die shows 2.

Step2: Find the required sum

We want the sum of the two dice to be 8. If the first die is 2, let the second - die value be \(x\). Then \(2 + x=8\), so \(x = 6\).

Step3: Calculate the probability

A die has 6 possible outcomes. Since the first die is already fixed as 2, and we want the second die to be 6, the probability that the second die shows 6 is \(\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)