Problem $6(4$ points$)$

Let $\backslash ($ M $\backslash )$ be an algorithm that solves a decision problem $\backslash (\backslash$Pi $\backslash )$ so that on every string $\backslash ($ x $\backslash ),$

$-$ if $\backslash ($ x $\backslash )$ is a "yes" instance of $\backslash (\backslash$Pi $\backslash ),$ then $\backslash ($ M $\backslash )$ returns the answer "yes" with probability $1$ ;

$-$ if $\backslash ($ x $\backslash )$ is a $"$no$"$ instance of $\backslash (\backslash$Pi $\backslash ),$ then $\backslash ($ M $\backslash )$ returns the answer $"$no$"$ with probability greater than $0$ and less than $1.$

Which of the following statements do you agree with? Select all that apply.

A$.$ The answer "yes" can be viewed as "definitely yes", which means that $\backslash ($ M $\backslash )$ returns this answer only on "yes" instances of $\backslash (\backslash$Pi $\backslash ).$

B$.$ The answer $"$no$"$ can be viewed as "definitely no$",$ which means that $\backslash ($ M $\backslash )$ returns this answer only on $"$no$"$ instances of $\backslash (\backslash$Pi $\backslash ).$

C$.$ The answer "yes" can be viewed as "probably yes", which means that $\backslash ($ M $\backslash )$ can return this answer in both cases: on "yes" instances of $\backslash (\backslash$Pi $\backslash )$ as well as on $"$no$"$ instances of $\backslash (\backslash$Pi $\backslash ).$

D$.$ The answer $"$no$"$ can be viewed as "probably no$",$ which means that $\backslash ($ M $\backslash )$ can return this answer in both cases: on "yes" instances of $\backslash (\backslash$Pi $\backslash )$ as well as on $"$no$"$ instances of $\backslash (\backslash$Pi $\backslash ).$