Ex 13.3, 13 - Chapter 13 Class 12 Probability (Term 2)
Last updated at Aug. 11, 2021 by Teachoo
Bayes theorem
Ex 13.3, 2 Important
Ex 13.3, 3
Misc 3
Ex 13.3, 4 Important
Ex 13.3, 9
Ex 13.3, 5
Ex 13.3, 13 (MCQ) Important You are here
Example 21 Important
Ex 13.3, 6 Important
Ex 13.3, 10 Important
Example 18 Important
Example 17 Important
Ex 13.3, 7
Ex 13.3, 8 Important
Example 19 Important
Ex 13.3, 11
Ex 13.3, 12 Important
Example 37 Important
Example 20 Important
Example 33 Important
Misc 12
Misc 16 Important
Misc 13 Important
Bayes theorem
Ex 13.3, 13 Probability that A speaks truth is 4/5 . A coin is tossed. A reports that a head appears. The probability that actually there was head is (A) 4/5 (B) 1/2 (C) 1/5 (D) 𝟐/𝟓Let E : A speaks truth F : A Lies H : head appears on the toss of a coin We need to find the Probability that head actually appears, if A reports that a head appears i.e. P(E|H) P(E|H) = "P(E) . P(H|E) " /"P(F) . P(H|F) + P(E) . P(H|E)" P(E) = Probability that A speaks truth = 4/5 P(H|E) = Probability that head appears, if A speaks truth = 1/2 P(F) = Probability that A lies = 1 – P(E) = 1 – 4/5 = 1/5 P(H|F) = Probability that head appears, if A lies = 1/2 Putting values in formula, P(E|H) = (4/5 × 1/2)/(1/5 × 1/2 + 4/5 × 1/2) = (1/5 × 1/2 × 4)/(1/5 × 1/2 [1 + 4]) = 4/5 Putting values in formula, P(E|H) = (4/5 × 1/2)/(1/5 × 1/2 + 4/5 × 1/2) = (1/5 × 1/2 × 4)/(1/5 × 1/2 [1 + 4]) = 4/5 Therefore, required probability is 4/5 ∴ A is the correct answer