Question: A doctor has decided to prescribe two new drugs D1and D2 to 200 heart patients such that 50 get drug D1, 50 get drug D2 and 100 get both. The 200 patients are chosen so that each had 80% chance of having a heart attack if given neither of the drugs. Drug D1 reduces the probability of a heart attack by 35 %, while drug D2 reduces the probability by 20%. The two drugs when taken together, work independently. If a patient, selected randomly from the chosen 200 patients, has a heart attack then the probability that the selected patient was given both the drug is:
Probability that patients who have been prescribed only drug D1 have a heart attack = 0.8 × 0.65 = 0.52
∴ 0.52 × 50 = 26 of these will have a heart attack.
Probability that patients who have been prescribed only drug D2 have a heart attack = 0.8 × 0.8 = 0.64
∴ 0.64 × 50 = 32 of these will have a heart attack.
Probability that patients who have been prescribed both drugs D1 and D2 have a heart attack = 0.8 × 0.65 × 0.8 = 0.416
∴ 0.416 × 100 = 41.6 of these will have a heart attack.
Hence, option (a).