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Example 4 In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in Class XII given that the chosen student is a girl? Total number of students = 1000 Total number of girls = 430 Girls studying in class XII = 10% of 430 = 10/100 Γ— 430 = 43 We need to find Probability that a student chosen randomly studies in class XII, given that the chosen student is a girl E: Student is in class XII F: Student is a girl We need to find P(E|F) Now, P(E ∩ F) = Probability student is a girl who is in Class XII = (π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘“π‘”π‘–π‘Ÿπ‘™ 𝑠𝑑𝑒𝑑𝑒𝑛𝑑𝑠 𝑖𝑛 πΆπ‘™π‘Žπ‘ π‘  " " 𝑋𝐼𝐼)/(π‘‡π‘œπ‘‘π‘Žπ‘™ π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝑆𝑑𝑒𝑑𝑒𝑛𝑑𝑠) = πŸ’πŸ‘/𝟏𝟎𝟎𝟎 And, P(F) = Probability student is a girl = πŸ’πŸ‘πŸŽ/𝟏𝟎𝟎𝟎 Now, P(E|F) = 𝑃(𝐸 ∩ 𝐹)/(𝑃(𝐹)) = (43/1000)/(430/1000) = 43/430 = 1/10 = 0.1

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.