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Two natural numbers n1 and n2 are chosen such that their sum equals 100. What is the probability that their product exceeds 1600?
- 20/33
- 58/99
- 13/33
- 59/99
Correct answer: 59/99
Solution
The product n1*(100-n1) > 1600 reduces to n1² - 100*n1 + 1600 < 0, which holds for 20 < n1 < 80, giving 59 valid values out of 99 total ordered pairs.
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