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Probability Ncert Solutions Maths class 12th Maths Class 12th Probability

89. Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduces 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.

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alok kumar singh | Contributor-Level 10

4 months ago

89. A patient has options to have the treatment of yoga and meditation and that of prescription of drugs.

Let these events be denoted by E1 and E2 i.e.,

E1 = Treatment of yoga and meditation

E2 = Treatment of prescription of certain drugs

P (E1) = P (E2) = 1/2

Let A denotes that a person has heart attack, then P (A) = 40% = 0.40

Yoga and meditation reduces heart attack by 30.

Inspite of getting yoga and meditation treatment heart risk is 70% of 0.40

P (A|E1) = 0.40 x 0.70 = 0.28

Also, Drug prescription reduces the heart attack rick by 25%

Even after adopting the drug prescription hear rick is 75% of 0.40

P (A|E2)&

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89. A patient has options to have the treatment of yoga and meditation and that of prescription of drugs.

Let these events be denoted by E1 and E2 i.e.,

E1 = Treatment of yoga and meditation

E2 = Treatment of prescription of certain drugs

P (E1) = P (E2) = 1/2

Let A denotes that a person has heart attack, then P (A) = 40% = 0.40

Yoga and meditation reduces heart attack by 30.

Inspite of getting yoga and meditation treatment heart risk is 70% of 0.40

P (A|E1) = 0.40 x 0.70 = 0.28

Also, Drug prescription reduces the heart attack rick by 25%

Even after adopting the drug prescription hear rick is 75% of 0.40

P (A|E2) = 0.40 x 0.75 = 0.30

$\begin{array}{l} P (E_{1} | A) = \frac{P (E_{1}) P (A | E_{1})}{P (E_{1}) P (A | E_{1}) + P (E_{2}) P (A | E_{2})} \\ = \frac{\frac{1}{2} \times 0.28}{\frac{1}{2} \times 0.28 + \frac{1}{2} \times 0.30} \\ = \frac{14}{29} \end{array}$

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