GATE CE 2024 Set 2 — Question 36
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Engineering Mathematics → Probability → Conditional Probability
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Question
In a sample of heart patients, each patient has 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 . Medicine X is taken by of these patients. The probability that a randomly selected patient, out of the patients, takes medicine X and has a heart attack is
Correct answer
(C) 20%
Solution
Let be the event that a patient takes medicine X, and be the event that a patient has a heart attack.Given:
Total patients
Patients taking medicine X,
Probability of heart attack without medicine,
Medicine X reduces the probability of heart attack by . This means the new probability is of the original probability:
We need to find the probability that a patient takes medicine X AND has a heart attack, which is :Thus, the correct option is (C).
Total patients
Patients taking medicine X,
Probability of heart attack without medicine,
Medicine X reduces the probability of heart attack by . This means the new probability is of the original probability:
We need to find the probability that a patient takes medicine X AND has a heart attack, which is :Thus, the correct option is (C).
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