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The probability that a pen manufactured by a company will be defective is 0.1. If 12 such pens are selected find the probability that i) exactly 2 will be detective ii) at least 2.will be defective iii)none will he defective
Asked by annapoornaa429 | 31 Mar, 2024, 08:23: PM

Probability of defective pd = 0.1 ; Probability of non-defective pnd = 0.9

Probabity of getting exactly two defective pen if 12 pens are chosen is obtained from binomial probability distribition.

Probabity p(2) of getting exactly two defective pen is

p(r=2) = 12C2 ( 0.1 )2 (0.9)10 = 0.230

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Probabity p(0) of not getting any defective pen is

p(r=0) = 12C0 ( 0.1 )0 (0.9)12 = 0.282

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Probabity p(r=1) of getting exactly one defective pen is

p(r=1) = 12C1 ( 0.1 )1 (0.9)11 = 0.377

Probability p(r ≥ 2 ) of atleast two defective pen out of 12 pen is

p(r ≥ 2 ) = 1 - p(r=0) - p(r=1) = 1 - 0.282 - 0.377 = 0.341

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Answered by Thiyagarajan K | 31 Mar, 2024, 10:46: PM

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