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Misc 13 - Assume chances of a patient having heart attack is 40%

Misc 13 - Chapter 13 Class 12 Probability - Part 2
Misc 13 - Chapter 13 Class 12 Probability - Part 3 Misc 13 - Chapter 13 Class 12 Probability - Part 4

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Misc 7 Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?Normal risk of heart attack is 40%. If we do meditation and yoga, it reduces risk by 30% i.e. risk becomes 40% Γ— 70% = 28% Let A : Person has heart attack E1 : Person is treated with meditation & yoga E2 : Person is treated with drug Given, P(A) = 40 % = 0.40 Also, given that meditation & yoga and drug has equal probabilities P(E1) = 1/2 , P(E2) = 1/2 We have to find that if a person selected has an heart attack, what is the probability that the person followed meditation & yoga. i.e. P(E1|A) P(E1|A) = (𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1))/(𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1)+𝑃(𝐸_2 ).𝑃(𝐴|𝐸_2) ) P(A|E1) i.e. Probability of having heart attack if he is treated with meditation Meditation reduce the risk by 30% , so there is a risk of 70% i.e 0.70 P(A|E1) = P(heart attack) Γ— Risk = 0.40 Γ— 0.70 = 0.28 P(A|E2) i.e. Probability of having heart attack if he is treated with drugs The daring reduce the risk by 25% , so there is a risk of 75% i.e. 0.75 P(A|E2) = P(heart attack) Γ— Risk = 0.40 Γ— 0.75 = 0.30 Therefore, P(E1|A) = (𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1))/(𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1)+𝑃(𝐸_2 ).𝑃(𝐴|𝐸_2) ) = (1/2 Γ— 0.28)/(1/2 Γ— 0.28 + 1/2 Γ— 0.30) = 0.28/(0.28 + 0.30) = 0.28/0.58 = 14/29

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.