$1.$Given the following Bayes network and conditional probabilities,

a$.$Now you are given a $$sampling machine$.$ This machine can be used for

generating a sample from distribution $($p$,1-$p$).$ The machine is deterministically

unstable: it returns the most likely value twice, the least value once, and repeats

this process forever. In case of sampling from a uniform distribution, it outputs

$$true$,$false$,$true$,$false$......$ For instance, if we use this machine to sample

from P$($A$),$ P$($A$),$ P$($D$),$ P$($D$),$ P$($A$),$ P$($D$),$ P$($B$|$A$=$true$),$ P$($B$|$A$=$true$),$ P$($B$|$A$=$true$)$ in

a row, the samples are true, false, true, true, true, false, false, false, true. Nodes

are selected in alphabet order to break a tie: A$-$D$-$B$-$C$-$E in our case.

Use this machine and Prior Sampling to generate $5$ samples. Show the samples

and then use the samples to compute P$($A$=$true, D$=$true, E$=$true$)$ and P$($B$=$true $|$

D$=$true, E$=$true$).$

Note that sampling from P$($B$|$A$=$t$)$ and sampling from P$($B$|$A$=$f$),$ as an example,

are two independent processes. Each of them has its own $$most likely twice,

least likely once$$ mechanism. $($Please provide the required steps for the answer$)$