Question 8 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by Teachoo

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Question 8 For any two events 𝐴 and 𝐵, if 𝑃(𝐴 ‾)=1/2,𝑃(𝐵 ‾)=2/3 and 𝑃(𝐴∩𝐵)=1/4, then 𝑃(𝐴 ‾/𝐵 ‾) equals: (A) 3/8 (B) 8/9 (C) 5/8 (D) 1/4Now, 𝑃(𝐴 ‾/𝐵 ‾ )=(𝑃(𝐴 ̅ ∩ 𝐵 ̅))/(𝑃(𝐵 ̅)) Using 𝑷(𝑨 ̅ ∩ 𝑩 ̅ )=𝑃((𝐴∪𝐵) ̅ ) =𝟏−𝑷(𝑨∪𝑩) Thus, 𝑷(𝑨 ‾/𝑩 ‾ )=(𝟏 − 𝑷(𝑨 ∪ 𝑩))/(𝑷(𝑩 ̅)) Finding 𝑷(𝑨∪𝑩) Given 𝑃(𝐴 ‾)=1/2,𝑃(𝐵 ‾)=2/3 and 𝑃(𝐴∩𝐵)=1/4 Now, 𝐏(𝐀)=1−𝑃(𝐴 ‾ ) =1−1/2 =𝟏/𝟐 Also, 𝐏(𝐁)=1−𝑃(𝐵 ‾ ) =1−2/3 =𝟏/𝟑 So, the correct answer is (C) Now, 𝑷(𝑨∪𝑩)=𝑃(𝐴)+𝑃(𝐵)−𝑃(𝐴∩𝐵) Putting values =1/2+1/3−1/4 =(6 + 4 − 3)/12 =𝟕/𝟏𝟐 Now, 𝑷(𝑨 ‾/𝑩 ‾ )=(1 − 𝑃(𝐴 ∪ 𝐵))/(𝑃(𝐵 ̅)) =(1 − 7/12)/(2/3) =(5/12)/(2/3) =5/12 ×3/2 =𝟓/𝟖 So, the correct answer is (C)

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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