Consider two independent random variables $\left(U_{1}, U_{2}\right)$ both are uniformly distributed between $[0,1]$. The conditional expectation
\[E\left[\left(U_{1}+U_{2}\right) \mid \max \left(U_{1}, U_{2}\right) \geq 0.5\right]\]
equals
- $7 / 6$
- $8 / 7$
- $6 / 7$
- $1.1$
- None of the above