Use the Bayesian Network below containing $6$ Boolean random variables to answer the following questions using inference by enumeration. For the problems,$=,=,=,=,=,$ and $=.$ Give your answers to $4$ decimal places, for uniformity. Show your work. Check your work using the Bayes$$ Java Script Program linked in Lecture $18.($a$)$ What is the probability that it rains? $(())($b$)$ What is the probability that the grass is wet? $(())($c$)$ Given that it is spring, how likely is there to be someone mowing? $((|))($d$)$ Given that it is spring, how likely is there to be a bird on the lawn? $((|))($e$)$ If there are birds on the lawn, but there are no worms out, how likely is it that it is spring? $((|,)),$ where the $$ denotes $$not$$ or $$complement$.$ The CPTs are defined as follows: $()=0\mathrm{.}25(|)=0\mathrm{.}6,(|)=0\mathrm{.}4(|)=0\mathrm{.}7,(|)=0\mathrm{.}2(|,)=0\mathrm{.}12,(|,)=0\mathrm{.}25,(|,)=0\mathrm{.}1,(|,)=0\mathrm{.}08(|)=0\mathrm{.}02,(|)=0\mathrm{.}42(|,)=0\mathrm{.}8,(|,)=0\mathrm{.}4,(|,)=0\mathrm{.}4,(|,)=0\mathrm{.}4$