dreamgmat1 wrote:

A point is arbitrarily selected on a line segment thus breaking it into two smaller segments.What is the probability that the bigger segment is at least twice as long as the smaller.

1/4

1/3

1/2

2/3

3/4

Think of the number line with the segment between 0 and 1, which point x chosen as cutting point.

The left segment is more than twice as long as the right if x > 2(1-x) i.e. x > 2/3

Thus the probability that the left segment is more than twice as long as the right is 1/3, as is the probability that the right is more than twice as logn as the left. So the required probability is 1/3 + 1/3 =2/3