Question

A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appeared at least once?

• A. \( \frac{1}{2} \)
• B. \( \frac{2}{3} \)
• C. \( \frac{3}{5} \)
• D. \( \frac{5}{6} \)

Hint:

Conditional probability can be computed using the formula \( P(A|B) = \frac{P(A \cap B)}{P(B)} \).

Answer 1

The Correct Option is B

Step 1: Conditional probability.
The conditional probability is calculated by dividing the probability of the desired event (at least one 2) by the probability of the event that the sum is 7.
Step 2: Conclusion.
Thus, the conditional probability is \( \frac{2}{3} \).
Final Answer: \[ \boxed{\frac{2}{3}} \]