You have recently invested in an electric skateboard. You always wear a helmet and padding to protect yourself (of course), but are worried that at some point you'll take a tumble and get scratched up. After assessing your skating ability, you estimate your probability of a crash on any single ride to be $0.005$.
I got this question while studying geometric and binomial distribution.
My current idea is
$1 - (P(x=0) + P(x=1) + P(x=2) + \ldots + P(x=9))$
where $x$ is the number of crashes, and get each probability by binomial distribution's formula.
I came up with this equation as I thought having $10$ or more crashes means same as not having $9$ or less crashes. Is my approach correct? Also, if it's correct, is there any way to simplify the calculation?