A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of 5 steps, he is one step away from the starting point.

Explanation

Since the man is one step away from starting point means that either

`(i) ` man has taken `6` steps forward aand` 5` steps backward

Or `(ii)` man has taken `5` steps forward and `6` steps backward.

Taking movement ` 1` step forward as success and `1` step backward as failure.

`therefore {p}=` Probability of success`=0.4` and `q= `probability of failure `=0.6`

`therefore ` required probability `={P}({X}=6 or X=5)`

`=P(X=6)+P(X=5)`

`=^{11} C_{6} p^{6} q^{5}+_{11} C^{5} p^{5} q^{6}`

...