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CMI-2020-DataScience-B: 8

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Owing to a defect in a certain machine which makes $N95$ masks, there is a $0.1\%$ probability that a mask it makes is $\text{not}$ effective in preventing airbone viruses from being inhaled.

  1. What is the probability that the first $1000$ masks that the machine produces are effective? (You may leave your solutions as arithmetic expressions; there is no need to compete their decimal representations).
  2. What is the probability that among the first one crore $(10^7)$ masks that the machine produces, there is at least one mask which is not effective?
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0.001 times mask is faulty and 0.999 times it is fine

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Part 1. All 1000 masks are effective

${0.999}^{1000}$ is the probability that the first 1000 masks are not faulty

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Part 2. All mask is effective : $0.999^{10000000}$

At least 1 is not effective : 1 – $0.999^{10000000}$

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