DSE 2011 Question 34: Random variables and standard distributions

Setup, from Q33 of the paper:

Suppose $X$ and $Y$ are independent random variables that follow the uniform distribution on the interval $[0,1]$. Let $Z=\min\{X,Y\}$. $\Pr(Z<0.5)$ (the probability that $Z$ is less than 0.5) equals

(Same setup: $X,Y$ i.i.d. $U[0,1]$, $Z=\min\{X,Y\}$.) $\Pr(Z<0.5\mid X=0.75)$ is