Problem $1$

Consider the Bayesian network:

Figure $1$ Bayesian network with probability transition: $t-$ True, $f-$ False

$($a$)$ If we hear alarm, what is the probability that it is caused by burglary but not earthquake?

$($b$)$ Our unaccountable neighbors may call us because of the alarm, or because of they just want to$.$

Calculate the probability that there was an alarm if you see you missed both John and Marry's call

$($c$)$ If we see we missed both John and Marry's call, what is the probability that there was a burglary but

not earthquake

Hint $1$: $p((B,E,A)|(J,M))+p((B,E,A)|(J,M))=p((B,E)|(J,M))$

Hint $2$: $p((J,M)|(B,E,A))=p((J,M)|A),p((J,M)|(B,E,A))=p((J,M)|A),$ because $J,M$ are

only directly caused by $A$ or $A$