Question

what is the probabilty that 0 doesnt appear among k digits chosen indepentantly and uniformy at random

Answer 1

Assuming we're working in base ten, the digits in question are $0,1,2,3,4,5,6,7,8,9.$

Suppose we take a group of $k$ digits, $d_1,d_2,...,d_k.$

What is the probability that $d_1\not=0$ ?

$$P_1(d_1\not=0)=\dfrac{9}{10}$$

$$P_2(d_1,d_2\not=0)=\dfrac{9}{10}(\dfrac{9}{10})=(\dfrac{9}{10})^2$$

$$...$$

$$P_k(d_1,d_2,...,d_k\not=0)=(\dfrac{9}{10})^k$$

The probabilty that doesn't appear among $k$ digits chosen indepentantly and uniformy at random is $(\dfrac{9}{10})^k$ .