GATE | GATE-CS-2014-(Set-1) | Question 65

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________
(A) 0.24 to 0.27
(B) 0.15 to 0.30
(C) 0.20 to 0.30
(D) 0.10 to 0.15


Answer: (A)

Explanation: The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.
Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit, which is answer.

Another approach –
See math.stackexchange.com/questions/350679/we-break-a-unit-length-rod-into-two-pieces-at-a-uniformly-chosen-point-find-the/350863#350863 for explanation

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