Conditional Probability - Statement

Chapter 13 Class 12 Probability (Term 2)
Concept wise

### 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 MCQβs be denoted by A2, & Difficult MCQβ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) = (πΈππ π¦ πππ’π πΉπππ π + πΈππ π¦ ππΆπ ππ’ππ π‘ππππ )/(πππ‘ππ ππ’ππ π‘ππππ ) = (300 + 500)/(300 + 200 + 500 + 400) = 800/1400 = 8/14 = 4/7 P(A2 + B2) = (πΈππ π¦ ππΆπ + π·ππππππ’ππ‘ ππΆπ ππ’ππ π‘ππππ )/(πππ‘ππ ππ’ππ π‘ππππ ) = (500 + 400 )/(300 + 200 + 500 + 400) = 900/1400 = 9/14 Also, (A2 + B2) β© (A2 + B2) = A2 So, P[(A2 + B2) β© (A2 + B2)] = P(A2 ) = 500/1400 = 5/14 Now, P((A1 + A2) | (A2 + B2)) = π[(π΄_1 + π΄_2 ) β© (π΄_2 + π΅_2 )]/π(π΄_2 + π΅_2 ) = (5/14)/(9/14) = 5/14 Γ 14/9 = 5/9 β΄ Required probability is π/π