Answer in Statistics and Probability for ash #205422
October 24th, 2022
what is the probabilty that 0 doesnt appear among k digits chosen indepentantly and uniformy at random
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_1not=0” ?
“P_1(d_1not=0)=dfrac{9}{10}”
“P_2(d_1,d_2not=0)=dfrac{9}{10}(dfrac{9}{10})=(dfrac{9}{10})^2”
“…”
“P_k(d_1,d_2,…,d_knot=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” .
