A man takes a step forward with probability 0.4 and backwards with a probability 0.6. Find the probability that after 11 steps he is just one step away from the starting point.

Hello student,

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.

Thanks and Regards

Shaik Aasif

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