# Ex 13.1, 13

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

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 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠𝑇𝑜𝑡𝑎𝑙 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠 = 300 + 500300 + 20 + 500 + 400 = 8001400 = 814= 47 P(A2 + B2) = 𝐸𝑎𝑠𝑦 𝑀𝐶𝑄 + 𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡 𝑀𝐶𝑄 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠𝑇𝑜𝑡𝑎𝑙 𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠 = 500 + 400 300 + 200 + 500 + 400 = 9001400= 914 Also, (A2 + B2) ∩ (A2 + B2) = A2 So, P[(A2 + B2) ∩ (A2 + B2)] = P(A2 ) = 5001400 = 514 Now, P((A1 + A2) | (A2 + B2)) = 𝑃 𝐴1 + 𝐴2 ∩ 𝐴2 + 𝐵2𝑃 𝐴2 + 𝐵2 = 514 914 = 514 × 149 = 59 ∴ Required probability is 𝟓𝟗

Chapter 13 Class 12 Probability

Serial order wise

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