100 pieces of paper in a box, one of which has a black dot on it. Probability Question. There are $100$ pieces of paper in a box, one of which has a black dot on it. If $100$ people go up one by one and pick a paper from the box, which one has the lowest probability of getting the black dot, and which one has the highest probability of getting the black dot?

The probability $p_k$ that the $k$-th person, $1\le k\le 100$ has the black dot is equal to $$p_k=\frac{99}{100}\cdot\frac{98}{99}\cdot\;\cdots\;\cdot\frac{100-(k-1)}{100-(k-1)+1}\cdot\frac{1}{100-k+1}=\frac1{100}$$ so it is independent of $k$ and equal for every one.
