A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is
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The man will be one step away from the starting point if (i) either he is one step ahead or (ii) one step behind the starting point.
∴ ∴ The required probability = P ( i ) + P ( ii )
The man will be one step ahead at the end of eleven steps if he moves six step forward and five steps backward.
The probability of this event is 
.
The man will be one step behind at the end of eleven steps if he moves six steps backward and five steps forward.
The probability of this event is 
.
Hence the required probability
.
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