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MHT CET202617 April 2026Evening ShiftMathematicsProbabilityActual

On average, one out of 10 persons is busy. If six persons are selected at random, then the probability that at least 5 of them will be busy is...

Options

  1. A25 (10)^6
  2. B35 (10)^6
  3. C45 (10)^6
  4. D55 (10)^6

Correct answer

D. 55 (10)^6

Step-by-step solution

The probability that a person is busy is p = 1 10 . The probability that a person is not busy is q = 1 - p = 9 10 . The number of persons selected is n = 6 . The probability that at least 5 persons are busy is P(X 5) = P(X = 5) + P(X = 6) . Using the binomial distribution P(X = r) = ^ n C_ r p^r q^ n-r : P(X = 5) = ⁶C₅ ( 1 10 )^5 ( 9 10 )^1 = 6 9 10^6 = 54 10^6 P(X = 6) = ⁶C₆ ( 1 10 )^6 ( 9 10 )^0 = 1 1 10^6 = 1 10^6 P(X 5) = 54 10^6 + 1 10^6 = 55 10^6 Answer: 55 (10)^6

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