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Previous Year Question (PYQs)



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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