It’s time for a random number duel! You and I will both use random number generators, which should give you random real numbers between 0 and 1. Whoever’s number is greater wins the duel!
There’s just one problem. I’ve hacked your random number generator. Instead of giving you a random number between 0 and 1, it gives you a random number between 0.1 and 0.8.
What are your chances of winning the duel?
$\dfrac{1}{10}$ of the time, I will win, as your number will be between 0 and 0.1.
$\dfrac{2}{10}$ of the time, I will lose, as your number will be between 0.8 and 1.
The remaining $\dfrac{7}{10}$ is random and fair.
Our respective chances of winning have a sum of 1, and difference of $\dfrac{1}{10}$.
Your chance of winning is $\dfrac{11}{20}$, mine is $\dfrac{9}{20}$.