Walk on the Cliff

A man is on the cliff. He is blindfolded and does not know where is the edge of the cliff. He can either take a step forwards or backwards at any one time. With every step, he gets further or closer to the edge of the cliff.

It is known that if he takes at least 2 steps towards the edge of the cliff, he will fall off. However, if he takes at least 4 steps away from the edge of the cliff, he will guarantee surviving.

What is the probability of the man surviving?

Assumptions:

• Each step is said to have equal distance.

• The edge of the cliff is either directly forward or directly behind the man.

• The man will go forward 50% of the time and go backward 50% of the time. His moves are absolutely random.