My doubt is on the following question from 2013 board paper:

Q: Assume that the chances of a patient having a heart attack is 40%. Assuming that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chance 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. Interpret the result and state which of the above stated methods is more beneficial for the patient.

The answer given to this board question was:

A: Let A, E1, and E2, respectively denote the events that a person has a heart attack, the selected person followed the course of yoga and meditation, and the person adopted the drug prescription.

Probability that the patient suffering a heart attack followed a course of meditation and yoga =

Now, calculate P(E2|A).

End of Answer~~

Now i come to my question. It says that A is the event the person has a heart attack, E1 is the event that he takes meditation course and E2 is the event that he takes drugs. Now, the statement "P(A|E1) = 70/100 * 40/100." is confusing since P(A|E1) is supposed to be event that the person suffers a heartattack given that he has taken yoga and meditation.

Now, as per the question, Yoga and Meditation will reduce the risk of heart attack by 30%, which means 30% of 40% (where 40% is the risk of person having a heart attack) = 12% , should be his current risk of heart attack (after doing yoga and meditation). Therefore P(A|E1) should be 12% (i.e 0.12), Am i not right? How did they take it to be 70/100 * 40/100? Please give a detailed explanation. Thanks in advance.

(Experts please help, I have unit test coming up soon).