Ex 13.5, 13 - Known that 10% articles manufactured are defective - Ex 13.5

13.5, 13 last slide.jpg

  1. Class 12
  2. Important Question for exams Class 12

Transcript

Ex 13.5, 13 It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective? In each of the following, choose the correct answer: Let X : be the number of defective articles Picking articles is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx n = number of articles = 12 p = Probability of getting defective articles = 10% = 10 100 = 1 10 q = 1 p = 1 1 10 = 9 10 Hence, P(X = x) = 12Cx (๐Ÿ/๐Ÿ๐ŸŽ)^๐’™ (๐Ÿ—/๐Ÿ๐ŸŽ)^(๐Ÿ๐Ÿโˆ’๐’™) We need to find Probability of getting 9 defective articles out of 12 i.e. P(X = 9) P(X = 9) = 12C9 (1/10)^9 (9/10)^(12 โˆ’ 9) = (12 !)/((12 โˆ’ 9) ! 9 !) (1/10)^9 (9/10)^3 = (12 ร— 11 ร— 10 ร— 9 !)/(3 ! 9 !) \ ร—1/ใ€–10ใ€—^9 (9/10)^3 = (12 ร— 11 ร— 10)/(3 ร— 2 ร— 1) ร— 1/ใ€–10ใ€—^9 (9/10)^3= (2 ร— 11)/ใ€–10ใ€—^8 9^3/ใ€–10ใ€—^3 = 22 (๐Ÿ—^๐Ÿ‘/ใ€–๐Ÿ๐ŸŽใ€—^๐Ÿ๐Ÿ )

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.