Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}.\frac{3}{4},\frac{1}{4},\frac{1}{8}.$ Then the probability that the problem is solbed correctly by at least one of them is
Answer & explanation
Correct answer: option 1
Required probability
$= 1-\left(1-\frac{1}{2}\right)\left(1-\frac{3}{4}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{8}\right)=1-\frac{1}{2}×\frac{1}{4}×\frac{3}{4}×\frac{7}{8}$
$=1-\frac{21}{256}=\frac{235}{256}$