$1.$ Na$$ve Bayes Nets $$ Using the probability statements about the training data provided below, compute the probabilities of each separate outcome class $($diamond$,$ heart, spade, club$)$ for the two test set observations shown on the next page. Show your work.

P$($diamond$)=0\mathrm{.}15$

P$($heart$)=0\mathrm{.}10$

P$($spade$)=0\mathrm{.}40$

P$($club$)=0\mathrm{.}35$

P$($gender $=$ male, major $=$ accounting, class year $=$ senior, favorite sport $=$ golf$)=0\mathrm{.}02$

P$($gender $=$ male, major $=$ economics, class year $=$ senior, favorite sport $=$ baseball$)=0\mathrm{.}01$

P$($gender $=$ female, major $=$ economics, class year $=$ junior, favorite sport $=$ football$)=0\mathrm{.}03$

P$($gender $=$ male $|$ diamond$)=0\mathrm{.}45$

P$($gender $=$ female $|$ diamond$)=0\mathrm{.}55$

P$($major $=$ accounting $|$ diamond$)=0\mathrm{.}20$

P$($major $=$ economics $|$ diamond$)=0\mathrm{.}02$

P$($class year $=$ senior $|$ diamond$)=0\mathrm{.}22$

P$($class year $=$ junior $|$ diamond$)=0\mathrm{.}26$

P$($favorite sport $=$ golf $|$ diamond$)=0\mathrm{.}21$

P$($favorite sport $=$ baseball $|$ diamond$)=0\mathrm{.}14$

P$($favorite sport $=$ football $|$ diamond$)=0\mathrm{.}62$

P$($gender $=$ male $|$ heart$)=0\mathrm{.}44$

P$($gender $=$ female $|$ heart$)=0\mathrm{.}56$

P$($major $=$ accounting $|$ heart$)=0\mathrm{.}08$

P$($major $=$ economics $|$ heart$)=0\mathrm{.}09$

P$($class year $=$ senior $|$ heart$)=0\mathrm{.}28$

P$($class year $=$ junior $|$ heart$)=0\mathrm{.}27$

P$($favorite sport $=$ golf $|$ heart$)=0\mathrm{.}22$

P$($favorite sport $=$ baseball $|$ heart$)=0\mathrm{.}29$

P$($favorite sport $=$ football $|$ heart$)=0\mathrm{.}48$

P$($gender $=$ male $|$ spade$)=0\mathrm{.}41$

P$($gender $=$ female $|$ spade$)=0\mathrm{.}59$

P$($major $=$ accounting $|$ spade$)=0\mathrm{.}08$

P$($major $=$ economics $|$ spade$)=0\mathrm{.}11$

P$($class year $=$ senior $|$ spade$)=0\mathrm{.}19$

P$($class year $=$ junior $|$ spade$)=0\mathrm{.}17$

P$($favorite sport $=$ golf $|$ spade$)=0\mathrm{.}25$

P$($favorite sport $=$ baseball $|$ spade$)=0\mathrm{.}35$

P$($favorite sport $=$ football $|$ spade$)=0\mathrm{.}32$

P$($gender $=$ male $|$ club$)=0\mathrm{.}70$

P$($gender $=$ female $|$ club$)=0\mathrm{.}30$

P$($major $=$ accounting $|$ club$)=0\mathrm{.}04$

P$($major $=$ economics $|$ club$)=0\mathrm{.}07$

P$($class year $=$ senior $|$ club$)=0\mathrm{.}25$

P$($class year $=$ junior $|$ club$)=0\mathrm{.}27$

P$($favorite sport $=$ golf $|$ club$)=0\mathrm{.}03$

P$($favorite sport $=$ baseball $|$ club$)=0\mathrm{.}19$

P$($favorite sport $=$ football $|$ club$)=0\mathrm{.}70$

Test data:

Obs # Gender Major Class Year Favorite Sport

$1$ male accounting senior golf

$2$ female economics junior baseball

$2.$ Does it make sense that P$($gender $=$ male $|$ diamond$)+$ P$($gender $=$ female $|$ diamond$)=1,$ but that P$($major $=$ accounting $|$ diamond$)+$ P$($major $=$ economics $|$ diamond$)1?$ Explain.

PLEASE ANSWER QUESTIONS IN DETAIL AND PROVIDE ALL CALCULATIONS BY HAND