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 :
Answer & explanation
Correct answer: option 1
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%
$P(Y/H)=\frac{P(H/Y)P(Y)}{P(H/Y)P(Y)+P(H/M)P(M)}$
$=\frac{33.75×50}{33.75×50+36×50}=\frac{15}{31}=\frac{135}{279}$