How many random picks will get you a pair of parallel lines ?
There are two urns titled M and C. They contain 10 tokens numbered 1 to 10. I draw token from each of the two urns at random and put it back into the urn. Every time I pick a number from the urn titled M and from the urn titled C I form a line
Y = M*X + C. At the most how many draws will ensure that there is at least one pair of parallel lines.
The answer is 11.
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1 solution
At the worst case in the 10 picks of M I can get numbers from 1 to 10. The 11th pick would be a number that already exists so when a line is generated it would be parallel to some other line. This is only in the worst case. In the best case a pair of lines thus generated can be parallel after two random picks. C is inconsequential.