Ex 13.3, 13 (MCQ) - Chapter 13 Class 12 Probability
Last updated at April 16, 2024 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 24 Important
Example 20 Important
Example 22 Important
Misc 6
Misc 10 Important
Misc 7 Important
Bayes theorem
Last updated at April 16, 2024 by Teachoo
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 Therefore, required probability is 4/5 ∴ A is the correct answer