One uniform beating three others

Let $X_1,\dots,X_{20}$ be independent $\text{Unif}(0,1)$ variables. What is $P\big(X_1>\max(X_2,X_{10},X_{15})\big)$?

$1/4$. The event says $X_1$ is the largest of the four variables $X_1,X_2,X_{10},X_{15}$. These are exchangeable, so each is equally likely to be the largest.