Problem 29 · AMC 8 Stretch
Core
Counting & Probability
and-process-multiply
A die is rolled 3 times. Find the probability that a 2 shows up all 3 times.
Show answer
Answer: 1/216
Show hints
Hint 1 of 3
Each roll is independent of the others — an AND process for probabilities.
Still stuck? Show hint 2 →
Hint 2 of 3
The chance of a 2 on one roll is \(1/6\). Multiply over the rolls.
Still stuck? Show hint 3 →
Hint 3 of 3
Compute \((1/6) \times (1/6) \times (1/6)\).
Show solution
Approach: AND process — multiply independent chances
- Each roll is independent, so multiply (AND process). The chance of a 2 each time is \(\frac{1}{6}\).
- So \(\left(\frac{1}{6}\right)^3 = \frac{1}{216}\).
Mark:
· log in to save