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Ex 13.5, 3 - There are 5% defective items in large bulk of items. What

Ex 13.5, 3 - Chapter 13 Class 12 Probability - Part 2
Ex 13.5, 3 - Chapter 13 Class 12 Probability - Part 3


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Ex 13.5, 3 There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item? If a trial is Bernoulli, then There is finite number of trials They are independenta Trial has 2 outcomes i.e. Probability success = P then Probability failure = q = 1 – P (4) Probability of success (p) is same for all trials Let X : be the number of defective items Picking items is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒^(π’βˆ’π’™) 𝒑^𝒙 Here, n = number of items = 10 p = Probability of getting defective item = 5% = 5/100 = 1/20 q = 1 – p = 1 – 1/20 = 19/20 Hence, P(X = x) = 10Cx (𝟏/𝟐𝟎)^𝒙 (πŸπŸ—/𝟐𝟎)^(𝟏𝟎 βˆ’ 𝒙) We need to find Probability that we get not more than one defective item P(not more than one defective item) = P(getting 0 defective item) + P(getting 1 defective item) = P(X = 0) + P(X = 1) = 10C0(1/20)^0 (19/20)^(10 βˆ’0) + 10C1(1/20)^1 (19/20)^(10 βˆ’ 1) = 1 Γ— 1 Γ— (19/20)^10 + 10 Γ— 1/20 Γ— (19/20)^9 = (19/20)^10+1/2 (19/20)^9 = 19/20 (19/20)^9+1/2 (19/20)^9 = (19/20)^9 [19/20+10/20] = (19/20)^9 29/20 = πŸπŸ—/𝟐𝟎 (πŸπŸ—/𝟐𝟎)^πŸ—

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.