A speaks truth in 80% cases and B speaks truth in 90% cases. In what percentage of cases are they likely to agree with each other in stating the same fact?

A speaks truth in 80% cases and B speaks truth in 90% cases. In what

Question 26 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2

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Question 26 A speaks truth in 80% cases and B speaks truth in 90% cases. In what percentage of cases are they likely to agree with each other in stating the same fact? Given P(A speaks truth) = 80% = 80/100 = 8/10 P(B speaks truth) = 90% = 90/100 = 9/10 Now, P( both agree) = P(both speak truth) + P(both speak false) = P(A speaks truth) × P(B speaks truth) + P(A speaks false) × P(B speaks false) = 8/10 × 9/10 + (1−8/10)×(1−9/10) = 8/10 × 9/10 + (2/10)×(1/10) = 72/100 + 2/100 = 74/100 ∴ Percentage of cases where they agree is 74%

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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.