Problem 9 · 2020 Math Kangaroo
Medium
Counting & Probability
complementary-counting
Two identical dice each have two red faces, two blue faces and two green faces. If both dice are rolled at the same time, what is the probability that the two top faces show different colours?
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Answer: E — 23
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Hint 1 of 2
Each die shows red, blue or green with equal chance 1/3.
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Hint 2 of 2
It is easier to find the chance the two match, then subtract.
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Approach: complementary counting on colours
- Each die shows each colour with probability 2/6 = 1/3.
- P(both same colour) = 3 × (1/3)·(1/3) = 1/3.
- P(different colours) = 1 − 1/3 = 2/3.
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