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BITSAT2016MathematicsProbabilityActual

A man takes a step forward with probability 0.4 and backward with probability 0.6 . The probability that at the end of eleven steps he is one step away from the starting point is

Options

  1. A2⁵ 3⁵ 5¹⁰
  2. B462 ( 6 25 )⁵
  3. C231 3⁵ 5¹⁰
  4. Dnone of these

Correct answer

B. 462 ( 6 25 )⁵

Step-by-step solution

As 0.4+0.6=1 , the man either takes a step forward or a step backward. Let a step forward be a success and a step backward be a failure. Then, the probability of success in one step =p=0.4= 2 5 The probability of failure in one step = q =0.6= 3 5 In 11 steps he will be one step away from the starting point if the numbers of successes and failures differ by 1 . So, the number of successes =6 The number of failures =5 or the number of successes =5 , The number of failures =6 the required probability = ¹¹ C ₆ p ⁶ q ⁵+

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