A man takes a step forward with probability 0.4 and backwards with probability 0.6 . Find the probab

Question

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

Professor PC Thomas Classes · Answer

Since the man is one step away from the starting point, he is either one step forward (or) one step backward from the starting point at the end of eleven step.\ If he is one step forward, then he has taken six steps forward and five steps backward.\ The man can take six steps forward in ${ }^{11} C_{6}$ ways.\ Therefore, probability that the man has taken six steps forward and five steps backward is ${ }^{11} C_{6}(0.4)^{6}(0.6)^{5}=462(0.4)^{6}(0.6)^{5}$\ Similarly, the probability that the man has taken five steps forward and six steps backward is\ ${ }^{11} C_{5}(0.4)^{5}(0.6)^{6}=462(0.4)^{5}(0.6)^{6}$\ The probability of required event is\ $462(0.4)^{6}(0.6)^{5}+462(0.4)^{5}(0.6)^{6}$\ $=462(0.4)^{5}(0.6)^{5}(0.4+0.6)=462(0.24)^{5}$