Bayesian Networks have shaped complicated issues with few knowledge and

resources. It is incorporated into the most cutting$-$edge technologies of the

modern day, including Articial Intelligence and Machine Learning.

$1.$Coin $1$ is a fair coin that comes up heads with probability $1/2.$

$2.$Coin $2$ is a biased coin that comes up heads with probability $1/4.$

$3.$Coin $3$ is a biased coin that comes up heads with probability $3/4.$

Question: Suppose you pick one of the coins uniformly at random and

ip it three

times. If you observe the sequence HHT $($where H stands for heads and

T stands for tails$),$ what is the probability that you chose Coin $3?$