Chapter 13 Class 12 Probability

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Transcript

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/πŸ“Let 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 = πŸ’/πŸ“ 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/πŸ“ P(H|F) = Probability that head appears, if A lies = 𝟏/𝟐 Putting values in formula, P(E|H) = (4/5 Γ— 1/2)/(1/5 Γ— 1/2 + 4/5 Γ— 1/2) = (1/5 Γ— 1/2 Γ— 4)/(1/5 Γ— 1/2 [1 + 4]) = 4/5 Therefore, required probability is 4/5 ∴ A is the correct answer

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.