Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2,…
2012
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?
- A.
10/21
- B.
5/12
- C.
2/3
- D.
1/6
Attempted by 52 students.
Show answer & explanation
Correct answer: B
Answer: 5/12
Reasoning: Split the outcomes by the value of the first roll.
If the first roll is 4, 5, or 6, there is no second roll. Only a first roll of 6 gives a sum at least 6, which has probability 1/6.
If the first roll is 1, 2, or 3 (each occurs with probability 1/6), you roll a second time. Compute the probabilities for each first-roll value:
First = 1: need second ≥ 5 → 2 favorable second-roll outcomes ⇒ probability (1/6)×(2/6) = 2/36.
First = 2: need second ≥ 4 → 3 favorable outcomes ⇒ (1/6)×(3/6) = 3/36.
First = 3: need second ≥ 3 → 4 favorable outcomes ⇒ (1/6)×(4/6) = 4/36.
Add these contributions: from first=6 get 1/6 = 6/36, and from first=1,2,3 get 2/36+3/36+4/36 = 9/36. Total = 6/36 + 9/36 = 15/36 = 5/12.