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Problem of the Day #172: Future Flash Floods September 7, 2011

Posted by Alex in : potd , trackback

In response to the flash flood that is coming tomorrow, Saketh is looking for shelter. He comes across Sreenath’s house, but Sreenath will only let Saketh stay in his house during the flood if Saketh can predict the height that the flood water will be. Saketh randomly chooses two real numbers in the range $[0, 10]$ and guesses every number in between. If the actual height of flood is a random number in the range $[0, 10]$ and Sreenath will accept Saketh’s guess if he is within $1$ unit of the answer, what is the probability that at least one of Saketh’s guesses will be accepted?

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