Q.49 From the database of a clinic it was found that out of 2000 patients who had visited
the clinic in a year, 900 had high BP, 900 had high Sugar and 400 had neither high
BP nor high Sugar. On a given day, if 20 patients visit the clinic, the expected
number of patients who have both high BP and high Sugar is _____ .
Problem Statement
The clinic probability problem tests set theory and expected value concepts crucial for CSIR NET Life Sciences examinations. Out of 2000 total patients:
- High BP cases: 900
- High sugar cases: 900
- Neither condition: 400
Question: Expected number of patients with both high BP and high sugar among 20 randomly selected daily visitors.
Problem Breakdown
Total patients with high BP or high sugar (or both):
\[ |A \cup B| = 2000 – 400 = 1600 \]
Patients with both conditions (using inclusion-exclusion):
\[ |A \cap B| = |A| + |B| – |A \cup B| = 900 + 900 – 1600 = 200 \]
Probability a patient has both conditions: \( \frac{200}{2000} = 0.1 \).
Expected value calculation (linearity of expectation):
\[ E[X] = n \times p = 20 \times 0.1 = 2 \]
Common Distractors
No options provided, but typical CSIR NET distractors include:
CSIR NET Relevance
This problem mirrors JAM/CSIR NET statistics questions on binomial expectation and set theory. Key insight: “Neither” directly gives the complement of the union, simplifying inclusion-exclusion calculations.
- Core Concepts: Probability, Expected Value, Inclusion-Exclusion Principle
- Exam Level: CSIR NET Life Sciences (Mathematical Methods section)
- Time Required: 2-3 minutes
- Marks: 2 marks
