# Ex 13.1, 13 - Chapter 13 Class 12 Probability (Term 2)

Last updated at Feb. 15, 2020 by

Last updated at Feb. 15, 2020 by

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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 + 200 + 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

Ex 13.1

Ex 13.1, 1

Ex 13.1, 2

Ex 13.1, 3 Important

Ex 13.1, 4

Ex 13.1, 5

Ex 13.1, 6 (i)

Ex 13.1, 6 (ii) Important

Ex 13.1, 6 (iii)

Ex 13.1, 7 (i)

Ex 13.1, 7 (ii)

Ex 13.1, 8

Ex 13.1, 9

Ex 13.1, 10 (a) Important

Ex 13.1, 10 (b) Important

Ex 13.1, 11

Ex 13.1, 12 Important

Ex 13.1, 13 Important You are here

Ex 13.1, 14

Ex 13.1, 15

Ex 13.1, 16 (MCQ) Important

Ex 13.1, 17 (MCQ) Important

Chapter 13 Class 12 Probability (Term 2)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.