Frequency-based (the right answer)
------------------------
p(positive) = 3/6 = 0.5
p(negative) = 3/6 = 0.5
p( I | positive ) = 4/13 = 0.308
p( hated | positive ) = 1/13 = 0.0769
p( that | positive ) = 2/13 = 0.154
p( movie | positive ) = 1/13 = 0.0769
p( loved | positive ) = 3/13 = 0.231
p( it | positive ) = 2/13 = 0.154
p( I | negative ) = 4/13 = 0.308
p( hated | negative ) = 3/13 = 0.231
p( that | negative ) = 2/13 = 0.154
p( movie | negative ) = 1/13 = 0.0769
p( loved | negative ) = 1/13 = 0.0769
p( it | negative ) = 2/13 = 0.154


p(I loved it | positive)= p(I | positive) p(loved | positive ) = p(it | positive) p(positive)
 = 4/13 * 3/13 * 2/13 * 0.5 = 0.005462

p(I thought I hated it but loved it | positive ) = 0 because p(thought | positive) = 0.  This is why we need to smooth!

Presence-based (close, but NOT the right answer)
p(positive) = 3/6 = 0.5
p(negative) = 3/6 = 0.5
p( I | positive ) = 3/3 = 1.0
p( hated | positive ) = 1/3 = 0.333
p( that | positive ) = 2/3 = 0.667
p( movie | positive ) = 1/3 = 0.333 
p( loved | positive ) = 3/3 = 1.0
p( it | positive ) = 2/3 = 0.667
p( I | negative ) = 3/3 = 1.0
p( hated | negative ) = 3/3 = 1.0
p( that | negative ) = 2/3 = 0.667
p( movie | negative ) = 1/3 = 0.333
p( loved | negative ) = 1/3 = 0.333
p( it | negative ) = 2/3 = 0.667