Probability
Probability
nta_abhyas_2025
Grade 12
Question:
A box contains tickets numbered $1$ to $N$ is tickets are drawn from the box with replacement. The probability that the largest number on the tickets is $k$, is
$\frac{k^n - (k-1)^n}{N^n}$
$\frac{k^n - (k-1)^n}{N^n}$
$\frac{k^n - (k-1)^n}{N^n}$
$\frac{k^n - (k-1)^n}{N^n}$
Step-by-Step Solution
Key Concept: Use combinatorics with replacement to count favorable outcomes where maximum value equals a specific number
The number of ways to select $k$ tickets from $N$ tickets with replacement is $N^k$. The largest number on selected tickets must be $k$, giving favorable outcomes as $k^k - (k-1)^k$. The required probability is $\frac{k^k - (k-1)^k}{N^k}$, which matches none of the given options exactly as stated.
Correct Answer: D