Probability that
Mark is successful = 1/4
Peter is successful = 2/5
Wanda is successful = 3/8
So, the probability that
$$Mark\ is\ not\ successful\ =\frac{4}{4}-\frac{1}{4}=\frac{\left(4-1\right)}{4}=\frac{3}{4}$$
$$Peter\ is\ not\ successful\ =\frac{5}{5}-\frac{2}{5}=\frac{\left(5-2\right)}{5}=\frac{3}{5}$$
$$Wanda\ is\ not\ successful\ =\frac{8}{8}-\frac{3}{8}=\frac{\left(8-3\right)}{8}=\frac{5}{8}$$
Probability that no student will get the answer correctly =
$$=\frac{3}{4}\cdot\frac{3}{5}\cdot\frac{5}{8}=\frac{\left(3\cdot3\right)}{4\cdot8}=\frac{9}{32}$$
Probability that at least one of the students was successful =
$$=\frac{1}{1}-\frac{9}{32}=\frac{\left(32-9\right)}{32}=\frac{23}{32}$$
Answer = option C