A Simple Question: DVD & Pre-Pro

I'm almost embarrassed to ask this question...

For the processing of Dolby Digital and DTS, is it necessary for both the DVD Player and the Pre-Pro to have the associated decoders?

Or, is it that the DVD player need only pass the 5.1 PCM stream to the DD & DTS decoders within the Pre-Pro?

I want to buy my daughter a DVD player, but am unsure whether I need to buy a pre-pro, as well, to hear the DD & DTS sound (I do know the differences between DD & DTS).

If I'm not asking the correct question, and you can figure
what the right question is, I would appreciate your help.

You only need one decoder. Most people pass the digital signal to the prepro. The one in the receiver/prepro typically has more features, flexibility with bass management, and perhaps higher quality.
The DVD player also need to be able to do it. My DVD player will play dolby digital but not dts.
You need DTS on the DVD player and the pre/pro if you wish to view movies in DTS
The first response from Inscrutable is the CORRECT one. Get a DVD player that also has DTS capability (most do now) but WITHOUT a decoder (for DD/DTS), and let the pre-pro decode the DD/DTS signal. You can get an excellent player now for as little as $225 retail (and that even gets you Progressive Scan), at Bust Buy and other stores. Also, The Secrets of Home Theatre site is an excellent source for info on DVD players.
There's a difference between being able to output the signal, and being able to decode it. It's best to leave the decoding to a processor, however the dvd player much be able to support (i.e. spit out) the dts or dd format. most dvd players these days can do that, and usually say so right on the faceplate or box (little dolby digital and dts logos).