Question

Mohan takes a step forward with probability 0.4 and backward with probability 0.6. If the probability that at the end of eleven steps Mohan is one step away from the starting point is k then the value of 5000k must be
A) 1750
B) 1850
C) 1900
D) 1950

Answer 1

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.