During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has 45% chance of having heart attack, but yoga and mediation assumed to reduce the chance of heart attack by 25% and 20% respectively. He has options to choose any of the two options with equal probabilities .If Amit goes through one of the two options selected at random and suffers a heart attack, then the probability that he had selected yoga is :

$\frac{135}{279}$

H → Chance of Heart attack

Y → Yoga

M → Meditation

P(H) = 45%

P(Y) = 50% = P(M)

P(H/Y) = 45% × (100 - 25%) = 33.75%

P(H/M) = 45% × (100 - 20%) = 36%

$P(Y/H)=\frac{P(H/Y)P(Y)}{P(H/Y)P(Y)+P(H/M)P(M)}$

$=\frac{33.75×50}{33.75×50+36×50}=\frac{15}{31}=\frac{135}{279}$