Problem 6 · 2024 Math Kangaroo
Medium
Counting & Probability
casework
Kaito has manipulated a die. The probabilities of rolling a 2, 3, 4 or 5 are still 16 each, but the probability of rolling a 6 is now twice the probability of rolling a 1. What is the probability of rolling a 6?
Show answer
Answer: D — 29
Show hints
Hint 1 of 2
The four fair faces use up a fixed total probability, leaving the rest for faces 1 and 6.
Still stuck? Show hint 2 →
Hint 2 of 2
Let P(1) be unknown, write P(6) = 2·P(1), and use that all six probabilities add to 1.
Show solution
Approach: use that all probabilities sum to 1
- Faces 2,3,4,5 each have probability 1/6, totalling 4/6 = 2/3.
- So P(1) + P(6) = 1 − 2/3 = 1/3.
- With P(6) = 2·P(1): 3·P(1) = 1/3, so P(1) = 1/9 and P(6) = 2/9.
Mark:
· log in to save