Question

assume that the chances of a patient having a heart attack is 40%. it is also a gym that a meditation and yoga course reduce the risk of heart attack by 30% and prescriptions of certain drugs produces its stance is by 25%. at a time of patient can choose any one of the two options with equal probability is it is given that after going through one of the two options the patient selected at random suffers heart attack find the probability that the patient followed of course of meditation and yoga ?


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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Assume that the chances of a patient having a heart attack is 40%. it is also a given that a meditation and yoga course reduce the risk of heart attack by 30% and prescriptions of certain drugs produces its chance is by 25%. At a time of patient can choose any one of the two options with equal probability. It is given that after going through one of the two options the patient selected at random suffers heart attack.

So, Let we assume that,

Let, E₁ be the event patient follows a course of mediation and yoga.

↝ E₂ be the event patient follows the prescription of certain drugs.

↝ E be the event the patient suffers a heartattack.

Then,

$\rm :\longmapsto\:P(E_1) = \dfrac{1}{2}$

$\rm :\longmapsto\:P(E_2) = \dfrac{1}{2}$

Now,

$\rm :\longmapsto\:P(E | E_1) = \dfrac{70}{100} \times \dfrac{40}{100} = \dfrac{28}{100}$

and

$\rm :\longmapsto\:P(E | E_2) = \dfrac{75}{100} \times \dfrac{40}{100} = \dfrac{30}{100}$

So, Required Probability the patient selected at random suffers heart attack, that the patient followed of course of meditation and yoga is

$\rm :\longmapsto\:P( E_1|E ) = \dfrac{P(E_1) . P(E | E_1)}{P(E_1) . P(E | E_1) + P(E_2) . P(E | E_2)}$

On substituting the values, we get

$\rm \:  =  \:\dfrac{\dfrac{1}{2} \times \dfrac{28}{100} }{\dfrac{1}{2} \times \dfrac{28}{100} + \dfrac{1}{2} \times \dfrac{30}{100} }$

$\rm \:  =  \:\dfrac{28}{28 + 30}$

$\rm \:  =  \:\dfrac{28}{58}$

$\rm \:  =  \:\dfrac{14}{29}$

Hence,

$\rm :\longmapsto\:P( E_1|E ) = \dfrac{14}{29}$

Answer 2

Answer:

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