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AP EAMCET201822 Apr 2018Evening ShiftMathematicsProbabilityActual

A manufacturer of locks knows that 2 % of his product is defective. If he sells the locks in boxes each with 100 locks and guarantees that not more than 2 locks will be defective in a box, then the probability that a box will fail to meet the guaranteed quality is

Options

  1. A1-5 e⁻²
  2. B_ k=2 ¹⁰⁰ ¹⁰⁰ C_k ( 1 50 )^k ( 49 50 )^ 100-k
  3. C0.02
  4. D1-3 e⁻²

Correct answer

A. 1-5 e⁻²

Step-by-step solution

The random variable is the number of defective locks with mean m=100 2 100 =2 So, the required probability aligned & =1-[P(r=0)+P(r=1)+P(r=2)] & =1- [e⁻² 2^ 0 ! +e⁻² 2^1 1 ! +e⁻² 2^2 2 ! ]=1-5 e⁻² aligned

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