# Let $X$ the number of random numbers selected of $\{0,1,2,…,9\}$ independently until the 0 comes out. find the probability function.

Let $X$ the number of random numbers selected of $\{0,1,2,...,9\}$ independently until the 0 comes out. find the probability function.

My work: Let $X=$"random number selected"
The sample space $S=\{b,ab,aab,...\}$ where $b=0$ and $a\in \{1,2,...,9\}$

Let $p:\mathbb{R}\rightarrow \mathbb{R}$ a probability function.

Note possible values $X$ can take is $X=1,2,3,4,5,6,7,8,9$ where $X=9$ can be taken only if $0$ never appear before.

Here i'm stuck. Can someone help me?

• Today I learned the word "aleatory". It means "random", and comes from "alea", the Latin word for dice. – Arthur May 27 '18 at 1:48
• What is the probability to select the sequence $a$ or $aaa$? – callculus May 27 '18 at 2:10
• It is much more simple. You have 10 possible outcomes. 9 of these outcomes are favorable. Then we use the classical definition of probability: $\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{9}{10}=0.9$ This is the probability to select not a 0: $a$. Then what is the probability to select $aaa$? – callculus May 27 '18 at 2:30
• oh... thanks @callculus very glad for your answer. – Bvss12 May 27 '18 at 2:35
• Consider geometric distribution. – BruceET May 27 '18 at 3:55