P(r/w) is the probability of picking a red rose at first picking and a white rose at second picking.
P(w/r) is the probability of picking a white rose at first picking and a red rose at second picking.
P(r/w) =
×
= 
P(w/r) =
×
=
Notice that the second fraction is out of 18 because the second picking of rose will be out of 18 since the first rose is not replaced.
P(r/w) equals to P(w/r)
P(w/r) is the probability of picking a white rose at first picking and a red rose at second picking.
P(r/w) =
P(w/r) =
Notice that the second fraction is out of 18 because the second picking of rose will be out of 18 since the first rose is not replaced.
P(r/w) equals to P(w/r)