Example 21 - A man is known to speak truth 3 out of 4 times - Bayes theoram

Slide14.JPG
Slide15.JPG

  1. Chapter 13 Class 12 Probability
  2. Serial order wise
Ask Download

Transcript

Example 21 A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. Let S1 : man speaks the truth S2 : man lies E : six on the die We need to find the Probability that it is actually a six, if the man reports that it a six i.e. P(S1|E) P(S1|E) = 𝑃 𝑆﷮1﷯﷯.𝑃(𝐸| 𝑆﷮1﷯)﷮𝑃 𝑆﷮1﷯﷯.𝑃(𝐸| 𝑆﷮1﷯)+𝑃 𝑆﷮2﷯﷯.𝑃(𝐸| 𝑆﷮2﷯)﷯ Putting value in formula, P(S1|E) = P(S1) . P(E|S1) ﷮P(S1) . P(E|S1) + P(S2) . P(E|S2)﷯ = 3﷮4﷯ × 1﷮6﷯﷮ 3﷮4﷯ × 1﷮6﷯ + 1﷮4﷯ × 5﷮6﷯ ﷯ = 1﷮4﷯ × 1﷮6﷯ × 3﷮ 1﷮4﷯ × 1﷮6﷯ 3 + 5﷯ ﷯ = 3﷮8﷯ Therefore, required probability is 𝟑﷮𝟖﷯

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.