Consider the following Bayesian network. It is set up to answer questions of the following type: "I'm at work, neighbor John calls to say my alarm is ringing, but neighbor Mary doesn't call. Sometimes it's set off by minor earthquakes. Is there a burglar?" The random variables B, E, A, J, and M are used for Burglary, Earthquake, Alarm, JohnCalls, and MarryCalls respectively.

Using this Bayesian network, calculate the following probabilities:

(a) P(A, J, M)

(b) P(A, M)

(c) P(M)

(d) P(B | M)

(e) P(B | M, J)

Burglary P(B) .001 Earthquake P(E) .002 BE E P(A B.E) T T .95 F .94 F T .29 F F .001 Alarm T AP(JA) JohnCalls I .90 F .05 MaryCalls A P( MA) T .70 F .01