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MHT CET · Maths · Probability

In a box containing 100 bulbs, 10 are defective. The probability that out of 20 bulbs selected at random, none is defective is

  1. A \(10\left(\frac{1}{10}\right)^{20}\)
  2. B \(20\left(\frac{9}{10}\right)^{20}\)
  3. C \(5\left(\frac{1}{10}\right)^{20}\)
  4. D \(\left(\frac{9}{10}\right)^{20}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left(\frac{9}{10}\right)^{20}\)

Step-by-step Solution

Detailed explanation

Let \(\mathrm{X}\) denote number of defective bulbs out of 20 bulbs \(\mathrm{p}=\) probability of getting defective bulb \(=\frac{10}{100}=\frac{1}{10}\) \(\therefore \mathrm{q}=1-\frac{1}{10}=\frac{9}{10}\) and \(\mathrm{n}=20\), Probability of getting no detective bulb is \(={ }^{20} \mathrm{C}_{0}\left(\frac{9}{10}\right)^{20}\left(\frac{1}{10}\right)^{0}=\left(\frac{9}{10}\right)^{20}\)