GATE DA 2025 Q61: Expected black balls in 100 draws with replacement

Probability and Statistics
2 marks
NAT
No negative marking

A bag contains 5 white balls and 10 black balls. In a random experiment, $n$ balls are drawn from the bag one at a time with replacement. Let $S_n$ denote the total number of black balls drawn in the experiment.

The expectation of $S_{100}$ denoted by $E[S_{100}] =$ ____ (Round off to one decimal place)

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 66.6 to 66.7 (official GATE 2025 final answer key)

Concept used: Expectation of a binomial random variable: $E[S_n] = np$ .

First step: Each draw is black with probability $\frac{10}{15} = \frac{2}{3}$ , independently, so $S_{100}$ is binomial with $n = 100$ .

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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GATE DA 2025 Q61: Expected black balls in 100 draws with replacement

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