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KCET2015MathematicsThree Dimensional Geometry

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

Options

  1. A(¹¹ C₅ (0.48)⁵ )
  2. B(¹¹ C₆ (0.24)⁵ )
  3. C(¹¹ C₅ (0.12)⁵ )
  4. D(¹¹ C₆ (0.72)⁶ )

Correct answer

B. (¹¹ C₆ (0.24)⁵ )

Step-by-step solution

Let, p= Probability that the man goes forward =0.4 And q= Probability that the man goes backward =0.6 So, p+q=1 Required event is, 5 p, 6 q or 6 p, 5 q So, required probability is given by n 5 p⁵ q⁶+ 11 6 p⁶ q⁵= 11 6 p⁵ q⁵(q+p)= 11 6 (p q)⁵= 11 6 (0.24)⁵

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