Visualization can make this problem a very easy one..

The catch word is ANY direction
We can infer that he would jump on the perimeter of a circle of radius 1 around it.

See the attached figure.
After taking the first jump on the circle say at point A as shown. The next two jumps can take the frog 2 m away from A.
Thus the Area of bigger circle, shaded in the sketch, is the total area where the frog can be, while the area of the smaller circle is the area where the frog is 1m from his initial position.
Required probability = \(\frac{\pi*1^2}{\pi*2^2}=\frac{1}{4}\)

C

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