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GATE 2024 CE (CE2) – Question 36

Engineering Mathematics · Probability and Statistics: Probability, conditional probability, descriptive statistics · 2 marks · Multiple choice

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

  1. 40%
  2. 60%
  3. 20%
  4. 30%

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Correct answer: (C) 20%

Explanation

The probability that a patient takes X is $\frac{50}{100} = 0.5$. With the medicine the chance of a heart attack is $0.8 \times 0.5 = 0.4$. So the probability of taking X and having a heart attack is $0.5 \times 0.4 = 0.2$, that is 20%.