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GATE 2024 BM – Question 28

Engineering Mathematics · Probability and Statistics · 1 mark · Numerical answer

Four people independently each have infection probability 0.1. Find the probability that at least two are infected, rounded to three decimals.

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Correct answer: 0.050 to 0.055

Explanation

Let X be Binomial(4,0.1). The complement includes zero and one infection: P(X≥2)=1−0.9⁴−4×0.1×0.9³=1−0.6561−0.2916=0.0523. Rounded to three decimals this is 0.052.

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