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In a box containing 60 bulbs, 6 are defective. What is the probability that out of a sample of 5 bulbs

(i) none is defective

(ii) exactly 2 are defective

1 Answer

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(i) Using Bernoulli’s Trial P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)

x = 0, 1, 2, ………n and q = (1 - p), n = 5

The probability of success, i.e. the bulb is defective \(=p=\frac{6}{100}=\frac{1}{10}\) \(q=1-\frac{1}{10}=\frac{9}{10}\)

probability of that no bulb is defective piece =

P(0 defective items) =

(ii) Using Bernoulli’s Trial P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)

x = 0, 1, 2, ………n and q = (1 - p), n = 5

The probability of success, i.e. the bulb is defective  \(=p=\frac{6}{60}=\frac{1}{10}\) \(q=1-\frac{1}{10}=\frac{9}{10}\)

probability of that there are exactly 2 defective pieces =

P(2 defective items) =

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