Problem 18 · 2015 Math Kangaroo
Hard
Counting & Probability
careful-counting
Bibi rolls a die which has the numbers 1, 2, 3, 4, 5, 6 on its faces. At the same time Tina rolls a die which has the numbers 2, 2, 2, 5, 5, 5 on its faces. Tina wins if she rolls a number higher than Bibi. What is the probability that Tina wins?
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Answer: C — 512
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Hint 1 of 2
Tina's die only ever shows 2 or 5; split into those two cases.
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Hint 2 of 2
Count Bibi's faces that each Tina value beats, over 36 equally likely pairs.
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Approach: case on Tina's roll, count favourable pairs out of 36
- There are 6×6 = 36 equally likely (Bibi, Tina) pairs.
- Tina rolls 2 (3 faces) and wins only against Bibi's 1: 3×1 = 3 wins.
- Tina rolls 5 (3 faces) and wins against Bibi's 1,2,3,4: 3×4 = 12 wins.
- Total 15 wins, so the probability is 15/36 = 5/12 (C).
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