Using the full joint probability distribution below, write out what the following probability distributions look like. Notice that the P is in boldface to emphasize that these are distributions (i. e., probability tables). This means you have to write out the probability distributions for all uninstantiated random variables e. g., for (a), write out P(Toothache, Cavity, Catch). Toothache Cavity Catch P(Toothache, Cavity, Catch)
false false false .576
false false true .144
false true false .008
false true true .072
true false false .064
true false true .016
true true false .012
true true true .108
A) P(Catch) (Note that this is a distribution, not a single number)
B) P(Toothache, Catch) (Note that this is a distribution, not a single number)
C) P(Toohache | Catch) (Note that this is a distribution, not a single number)