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?

Slide74.JPG

Slide75.JPG

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

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%

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.