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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.

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.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
9 years ago
Hello Student,
Please find the answer to your question
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
askIITians Faculty

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