In a certain test, 5% of patients have a disease. The test is positive for 90% of diseased and 10% of healthy. If a patient tests positive, the probability they have the disease is about: MCQ with Answer and Explanation

In a certain test, 5% of patients have a disease. The test is positive for 90% of diseased and 10% of healthy. If a patient tests positive, the probability they have the disease is about:
A. 0.50
B. 0.10
C. 0.90
D. 0.32
Answer: Option D
Solution (By JKSSB Mock Tests)
P(D)=0.05, P(+|D)=0.9, P(+|D')=0.1. P(D|+) = (0.05×0.9) / (0.05×0.9 + 0.95×0.1) = 0.045/(0.045+0.095)=0.045/0.14≈0.321.

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The cost of living index number for 2022 with base 2015 is 150. This implies that a household which spent Rs. 10,000 per month in 2015 needs to spend ______ in 2022 to maintain the same standard of living.
A. Rs. 11,500
B. Rs. 10,000
C. Rs. 12,500
D. Rs. 15,000

Correct Answer: Option D


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Cost of Living Index 150 means the cost has increased by 50%, so new cost = 10,000 × 1.5 = 15,000.

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Question #2
The multiplication theorem for independent events states P(A ∩ B) = P(A) × P(B). For dependent events, it becomes:
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D. Both B and C are correct

Correct Answer: Option D


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For any events, P(A∩B) = P(A|B)P(B) = P(B|A)P(A); independence is the special case where P(A|B)=P(A), reducing to P(A)P(B).

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