Four persons independently solve a certain problem correctly with...

$P$(Problem solved by at least one) $= 1 - P$(Problem is not solved by all)

$= 1 - P\left(\overset{¯}{A}\right)P\left(\overset{¯}{B}\right)P\left(\overset{¯}{C}\right)P\left(\overset{¯}{D}\right)$

$= 1 - \left(\dfrac{1}{2}\right)\left(\dfrac{1}{4}\right)\left(\dfrac{3}{4}\right)\left(\dfrac{7}{8}\right) = 1 - \dfrac{21}{256} = \dfrac{235}{256}$