Passage: A 4-digit number is selected at random formed by using the digits $0$, $1$, $2$, $3$ and $4$ (where repetition of digits is not allowed).

Question: What is the probability that the number selected does not contain zero at any position ?

The total number of $4$-digit numbers formed using the digits $0, 1, 2, 3, 4$ without repetition is calculated by filling the thousands place in $4$ ways (excluding $0$) and the remaining $3$ places in $^{4}P_{3}$ ways.

Total outcomes = $4 \times 4 \times 3 \times 2 = 96$

The number of $4$-digit numbers formed without using $0$ at any position means using only the digits $1, 2, 3, 4$.

Favorable outcomes = $^{4}P_{4} = 4 \times 3 \times 2 \times 1 = 24$

Required probability = $\dfrac{24}{96} = \dfrac{1}{4} = 0.25$

Answer: $0\cdot25$