1983 AHSME Problems/Problem 15
Problem
Three balls marked and are placed in an urn. One ball is drawn, its number is recorded, and then the ball is returned to the urn. This process is repeated and then repeated once more, and each ball is equally likely to be drawn on each occasion. If the sum of the numbers recorded is , what is the probability that the ball numbered was drawn all three times?
Solution
Since a ball is drawn three times and the sum is , the only ways this can happen are the permutations of and . Therefore, with there being equally-likely possibilities in total, the probability that the ball numbered was drawn all three times is .
See Also
1983 AHSME (Problems • Answer Key • Resources) | ||
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Followed by Problem 16 | |
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