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 perscription 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 probabihty that the pabent followed a course of meditation and yoga?

.: ${E_1}:$ Patient follows meditation and Yoga
${E_2}:$ Patient uses drug and $A$

: Patient suffers a heart attack.

$\therefore$ $P\left( {{E_1}} \right) = P\left( {{E_2}} \right) = \cfrac{1}{2},P(A) = 40\% = 0.4$

Also, $P\left( {A|{E_1}} \right) = \cfrac{{40}}{{100}}\left( {1 - \cfrac{{30}}{{100}}} \right) = \cfrac{{28}}{{100}}$

( Yoga \& meditation reduces heart attack by 30\%)
and $P\left( {A|{E_2}} \right) = \cfrac{{40}}{{100}}\left( {1 - \cfrac{{25}}{{100}}} \right) = \cfrac{{30}}{{100}}$

( drug prescription reduces heart attack by $25\%$ )
By Baye's theorem,

$P\left( {{E_1}|A} \right) = \cfrac{{P\left( {{E_1}} \right) \cdot P\left( {A|{E_1}} \right)}}{{P\left( {{E_1}} \right)P\left( {A|{E_1}} \right) + P\left( {{E_2}} \right)P\left( {A|{E_2}} \right)}}$

$= \cfrac{{\left( {\cfrac{1}{2}} \right)\left( {\cfrac{{28}}{{100}}} \right)}}{{\left( {\cfrac{1}{2}} \right)\left( {\cfrac{{28}}{{100}}} \right) + \left( {\cfrac{1}{2}} \right)\left( {\cfrac{{30}}{{100}}} \right)}}$

$= \cfrac{{28}}{{28 + 30}} = \cfrac{{28}}{{58}} = \cfrac{{14}}{{29}}$