Question

Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?

Accepted Answer

The correct answer is (B) 5/12. If the first roll is 4, 5, or 6 (no second roll), the sum is just that value, which is ≥6 only for the outcome 6: contributes 1/6. If the first roll is 1, 2, or 3 (prob 1/6 each), a second roll happens and the sum needs the second roll to be ≥ (6−first): first=1 needs second≥5 (2/6), first=2 needs second≥4 (3/6), first=3 needs second≥3 (4/6). This contributes (1/6)(2/6)+(1/6)(3/6)+(1/6)(4/6) = 9/36 = 1/4. Total = 1/6 + 1/4 = 2/12 + 3/12 = 5/12.

Explanation