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MHT CET20239 May 2023Evening ShiftMathematicsProbabilityActual

A man takes a step forward with probability 0.4 and backwards 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. A¹¹ C ₆(0.24)^6
  2. B¹¹ C ₆(0.4)^6(0.6)^5
  3. C¹¹ C ₆(0.24)^5
  4. D¹¹ C ₆(0.4)^5(0.6)^6

Correct answer

B. ¹¹ C ₆(0.4)^6(0.6)^5

Step-by-step solution

Let a step forward be a success and the step backward be a failure. Probability of success = p =0.4 , and Probability of failure =q=0.6 Now, in 11 steps number of successes =6 , number of failure =5 OR number of successes =5 , number of failures =6 Required probability = ¹¹ C ₆ p ^6 q ^5+ ¹¹ C ₅ p ^5 q ^6 . aligned & = 11 ! 6 ! 5 ! p^6 q^5+ 11 ! 5 ! 6 ! p^5 q^6 & = ¹¹ C₆ p^5 q^5(p+q) & = ¹¹ C₆(0-4)^5(0-6)^5(1) & = ¹¹ C₆(0 4)^5(0 6)^5 & = ¹¹ C₆(0 24)^5 aligned

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