Answer to Question #205422 in Statistics and Probability for ash

Question #205422

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


1
Expert's answer
2021-06-11T02:47:40-0400

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" .



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