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A person moves one unit forward with probability 0.4 and one unit backward with probability 0.6. After 11 such moves, the probability that he is exactly one unit from his starting position is
- 2⁵ 3⁵ / 5¹⁰
- 462 × (6/25)⁵
- 231 × 3⁵ / 5¹⁰
- none of these
Correct answer: 462 × (6/25)⁵
Solution
To be one unit away after 11 moves: (F=6,B=5) or (F=5,B=6). Probability = C(11,6)(0.4^6 0.6^5 + 0.4^5 0.6^6) = 462*0.4^5*0.6^5 = 462*(6/25)^5.
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