Probability --- overlaps of segments

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Inside a line segment E with length 1 unit , there are 2 segments A with length 1/3 unit and B with length 1/2 unit . The position of A is fixed with its left end being k unit from the left end of E(Thus the distance between their right ends will be (2/3 −k) unit),while B can move freely and uniformly inside E . A point is chosen randomly on E , if the probability that the point lies inside A and B at the same time = 1/4 , find the values of k . (in fractions)

mr.wong