Problem 23 · 2010 Math Kangaroo
Stretch
Counting & Probability
careful-counting
I roll an ordinary die three times. What is the probability that I rolled a ‘2’ at least once, given that the third number is equal to the sum of the first two?
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Answer: D — \(\frac{8}{15}\)
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Hint 1 of 2
The condition limits the first two rolls so their sum is still a die face.
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Hint 2 of 2
List those equally likely outcomes, then count the ones showing a 2.
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Approach: conditional probability by listing valid outcomes
- The third number equals the first two's sum, so that sum must be at most 6; there are 15 such (first, second) pairs.
- Among the three numbers (the two rolls and their sum), count those containing a 2: there are 8.
- The conditional probability is 8/15.
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