GATE 2025 DA – Question 61
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*)
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Show answer and explanation
Correct answer: 66.37 to 67.03
Explanation
With replacement, each draw is black with the same probability $\frac{10}{15} = \frac{2}{3}$, so $S_{100}$ is binomial and $E[S_{100}] = 100 \times \frac{2}{3} = 66.7$.