The DM doesn't have to tell you the odds. You've got a character sheet and will generally add a number to the die based on how skilled your character is. After you roll the die, the DM will tell you if you succeeded or not.
In some games, and for some rolls (like "Insight", "Sense Motive", "Perception", etc), they won't even give you that much - they'll roll for you where you can't see the number, and then give you information accordingly.
There are some rolls which are WAY too easy to metagame just from the result ("I rolled a 1, I'm totally not going to trust anything the GM tells me!"), where it can actually be way more fun if the GM rolls for you so you have no idea whether you rolled low or high, and if you roll low, they can actively lie to you.
"Yes, while you were initially suspicious of Mr. Sinastrov McEvilface, in retrospect you get the feeling that he's actually quite trustworthy, and is probably telling you the truth about the Definitely Not a Trap Inn, and how you should go there to meet with his contact, Bob Absolutelynotgoingtotryandkillyouson."
Some GMs may do the same thing if a bad guy is using spells like Charm Person or something similar, where rather than having you roll your saving throw (and thus knowing for sure something bad likely just happened if you roll low), they'll just roll for you and then subtly encourage you to like/trust an NPC by how they play them, or just slip you a note so YOU know what happened but the other players don't.
In my experience the DM rolling for a player isn't very common at all. Perception is probably the single most common skill check I've had to make. My point was mostly just that community episode was just misleading in that respect. ---
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