Problem $4(8$ points$)$: Study the following Bayesian Network, where variables are all Boolean$-$valued and then answer the questions$($show your work$)$:

Figure $14\mathrm{.}2$ A typical Bayesian network, showing both the topology and the conditional probability tables $($CPTs$).$ In the CPTs$,$ the letters $B,E,A,J,$ and $M$ stand for Burglary, Earthquake, Alarm, JohnCalls, and MaryCalls, respectively.

$1-$ Calculate the value of $P(A,B,E,J)$ :

$2-$ What is the probability of Burglary or Earthquake:

$3-$ What will the probability of John calling if we already know that there were a Burglary but there were no Earthquake: