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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. |
Answer» Since the man is one step away from starting point means that either (i) man has taken 6 steps forward aand 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) = 11C6 p6 q5 + 11C5 p5q6 = 11C5 (p6q5 + p5q6) = 11C5 (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 |
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