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Previous Year Question (PYQs)
3
A box contains tickets numbered $1$ to $N$.
Let $X$ be the largest number drawn in $n$ random drawings with replacement.
Then the probability $P(X = k)$ is:
Solution
$P(X \le k) = (k/N)^n$
$P(X \le k-1) = ((k-1)/N)^n$
So,
$P(X = k) = P(X \le k) - P(X \le k-1)$
$= (k/N)^n - ((k-1)/N)^n$
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