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Consider 5 independent Bernoulli's trials each with probability of success p . If the probability of at least one failure is greater than or equal to 31 32 , then p lies in the interval

Options

  1. A( 3 4 , 11 12 ]
  2. B[0, 1 2 ]
  3. C( 11 12 , 1 ]
  4. D( 1 2 , 3 4 ]

Correct answer

B. [0, 1 2 ]

Step-by-step solution

n =5 Success = p Failure = q P (at least one failure) 31 32 1- P (no failure) 31 32 1- P ( x =5) 31 32 1- ^5 C ₅ p ^5 31 32 - p ^5 - 1 32 p ^5 1 32 p 1 2 p [0, 1 2 ]

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