why is the binomial tree valuation different under the derivatives section vs. fixed income section

For example why do we incorporate up/down movements and also probabilties with each in the dervitives binomial tree, but we do not see this in the fixed income section?

In derivatives, do you mean for options?

yes

If I remember correctly… In fixed income the int rates are set in such a way that the risk neutral probabilities would come out to be .5 or 50% therefore most questions would move forward with an assumed .5 probab for up move and down move each…

Probably for much the same reasons that some countries have people drive on the right side of the road while others have them drive on the left side of the road: each group (in this case, fixed income analysts and derivatives analysts) developed their own way of doing it without consulting the other.

One decided to fix the prices and adjust the weights, while the other decided to fix the weights and adjust the prices (or, in this case, the interest rates). Not a big deal.