Ex 13.1, 13 - An instructor has a question bank of 300 easy - Ex 13.1

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  1. Chapter 13 Class 12 Probability
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Ex 13.1, 13 An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question? Let easy True/False questions be denoted by A1, difficult True/False questions be denoted by B1, easy MCQ’s be denoted by A2, & difficult MCQ’s be denoted by B2, Given, A1 = 300 , B1 = 200 , A2 = 500 , B2 = 400 A question is selected at random We need to find the probability that it will be an easy question, given that it is a MCQ. i.e. P((A1 + A2) | (A2 + B2)) Now, P(A1 + A2) = 𝐸𝑎𝑠𝑦 𝑇𝑟𝑢𝑒 𝐹𝑎𝑙𝑠𝑒 + 𝐸𝑎𝑠𝑦 𝑀𝐶𝑄 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠﷯ = 300 + 500﷮300 + 20 + 500 + 400﷯ = 800﷮1400﷯ = 8﷮14﷯= 4﷮7﷯ P(A2 + B2) = 𝐸𝑎𝑠𝑦 𝑀𝐶𝑄 + 𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡 𝑀𝐶𝑄 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠﷯ = 500 + 400 ﷮300 + 200 + 500 + 400﷯ = 900﷮1400﷯= 9﷮14﷯ Also, (A2 + B2) ∩ (A2 + B2) = A2 So, P[(A2 + B2) ∩ (A2 + B2)] = P(A2 ) = 500﷮1400﷯ = 5﷮14﷯ Now, P((A1 + A2) | (A2 + B2)) = 𝑃 𝐴﷮1﷯ + 𝐴﷮2﷯﷯ ∩ 𝐴﷮2﷯ + 𝐵﷮2﷯﷯﷯﷮𝑃 𝐴﷮2﷯ + 𝐵﷮2﷯﷯﷯ = 5﷮14﷯﷮ 9﷮14﷯﷯ = 5﷮14﷯ × 14﷮9﷯ = 5﷮9﷯ ∴ Required probability is 𝟓﷮𝟗﷯

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.