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A point is selected at random from the interval (0; 1); it then divides this interval into two segments. What is the probability that the longer segment is at least twice as long as the shorter segment?

Do we treat it as a uniform random variable and use the normalization rule to get f(x) and F(x)? I'm not really sure.

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    Could you give a title which indicates what the question is about?2012-09-19

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Think: which points will divide the interval into two segments, one at least twice as long as the other? and, what is the probability then of choosing one of those points?

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    The points between 0 and 1/3, together with the points between 2/3 and 1, constitute two-thirds of the interval $(0,1)$; *that* means there's a 2 out of 3 chance.2012-09-20