GATE 2022 BM – Question 32
In the source’s simplified model, three family members independently have equally likely positive or negative COVID status. Given that one member has tested positive, find the conditional probability that at least two are positive, rounded to three decimals.
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Correct answer: 0.570 to 0.572
Explanation
The official interpretation is that at least one of the three is positive, without identifying a particular member in advance. Of eight equally likely status patterns, seven satisfy this condition. Four of these have at least two positives: three with exactly two and one with three. Probability=4/7=.571. If a predetermined named member were known positive, the probability would instead be .75; the source’s wording is ambiguous, and the official interval uses the former reading.