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# 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 steps he is one step away from the starting point.

Jitender Pal
7 years ago
Hello Student,
Since the man is one step away from starting point means that either
(i) man has taken 6 steps forward and 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.
∴ p = Probability of success = 0.4 and q = probability of failure = 0.6
∴ Required probability = P (X = 6 or X = 5)
= P (X = 6) + P (X = 5)
= 11 C6 p6 q5 + 11 C5 p5 q6
= 11 C5 (p6 q5 + p5 q6) = 11 C5 (p + q) (p5 q5)
= 11. 10. 9. 8. 7/1. 2. 3. 4. 5 (0.4 + 0.6) (0.4 x 0.6)5
= 462 x 1 x (0.24)5 = 0.37
Hence the required prob. = 0.37
Thanks
Jitender Pal