I was studying from a website where there are 100 questions (numbered from 1-100). I was using a random number generator everytime (uniform distribution from 1-100) to choose the question I will solve next to keep my study session exciting. I will stop my study session as soon as I encounter a question I have seen before. How many questions on an average will I be doing ?
2026-04-02 01:27:23.1775093243
expected number of questions todo
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Hint:
$P(First \: repeat \: is \: on \: nth \: problem) = (1 \cdot\frac{99}{100} \cdot \frac{98}{100}\cdot...\cdot \frac{100-n+2}{100}\frac{n-1}{100})$
$Average \: number \: of \: questions = $ $$\sum_{n=1}^{100} P(First \: repeat \: is \: on \: n'th \: problem) \cdot n$$