simple EV calculation

HU on the river and I'm first to act, I want to compare the EV of betting to that of check/calling.

Board:A3342 (no flush possibility)

I hold AT and am first to act

My opponents range: AJ (8ways),AQ(8),AK(8),KK(6),QQ(6)

Assume if I bet he never raises me.

X=%he calls with KK,QQ
Y=% he calls with AJ,AQ,AK

EV betting= X(12/36)(+1) + Y(24/36)(-1)

P=% he bets KK,QQ if I check
Z=% he bets AJ,AQ,AK if I check

EV check/call=P(12/36)(+1) + Z(24/36)(-1)


Is this right?