solution for:

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

One step away means a step forward or a step backward
=> either he took 6 forward steps and 5 backward steps or 6backward steps and 5 forward steps
=> reqd. probability
= 11C6 * (0.4)^6 * (0.5)^5 + 11C6 * (0.4)^5 * (0.6)^5
= 11C5 * (0.4)^5 * (0.6)^5 * (0.4 + 0.6) ... [11C6 = 11C5]
= (11x10x9x8x7)/(1x2x3x4x5) * (0.24)^5
= 0.368