Problem 9 · 2017 Math Kangaroo
Medium
Counting & Probability
careful-counting
In each of the five boxes (A) to (E) there are red and blue balls. Benedict wants to take exactly one ball, without looking, out of one of these boxes, and hopes to get a blue ball. In which box is the probability of that happening greatest?
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Answer: B — 6 blue, 4 red
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Hint 1 of 2
For each box the chance of a blue ball is blues divided by total balls.
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Hint 2 of 2
Compare the five fractions and pick the largest.
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Approach: compare the blue fractions
- The chances are 10/18, 6/10, 8/14, 7/14, 12/21.
- As decimals: 0.56, 0.60, 0.57, 0.50, 0.57.
- The greatest is 6/10 = 0.60, which is box B.
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