Two small rivers A and B meet and become a larger river C$.$ For a new housing project, the flood level, defined as the water

level above the mean level of river $C,$ is under consideration. Past records indicate that a $1-$ft change in the water

level of river A causes a $0\mathrm{.}5ft$ change in the water level of river $C,$ and a $1ft$ in the water level of river $B$ causes a

$0\mathrm{.}25ft$ change in water level of river C$.$ The flood levels of rivers A and B can be estimated precisely. However, they

are equally likely to be $0,1,2$ and $3ft$ for both rivers. Assuming statistical independence of flood levels between rivers

A and B$,$ what is the probability that the flood level of river $C$ will exceed $2ft?$