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In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by 50%. Medicine X is taken by 50 of these 100 patients. The probability that a randomly selected patient, out of the 100 patients, takes medicine X and has a heart attack is
- 40%
- 60%
- 20%
- 30%
Correct answer: 20%
Solution
The probability of a patient having a heart attack without medicine X is 80%. With medicine X, this risk is reduced by 50%, resulting in a 40% chance of having a heart attack for those taking the medicine. Since 50 out of 100 patients take the medicine, the overall probability of a randomly selected patient taking medicine X and having a heart attack is 50% of 40%, which equals 20%.
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