$11.$ An investor holds two stocks, each of which can rise $($R$),$ remain unchanged $($U$),$ or decline $($D$)$ on any particular day.

Assume that for the first stock

P$($R$)=\mathrm{.}5,$ P$($U$)=\mathrm{.}1,$ P$($D$)=\mathrm{.}4$

and that for the second stock

P$($R$)=\mathrm{.}7,$ P$($U$)=\mathrm{.}2,$ P$($D$)=\mathrm{.}1$

and assume that movements of the two stocks are independent.

A$)$ Let x equal the number of stocks that rise on a particular day. Write the probability distribution for x$.$B$)$ What is the probability that the second stock does not rise if the first stock rises? C$)$ What is the probability that neither stock rises? $...$ Please answer this fully showing step by step how to solve it$,$ thank you!