Ytukyg

Probability of being dealt pairs

$4P2 * 13over 52P2$ = 5.88%, 4 different ways to choose from and arrange 4 cards from a suit times thirteen suits.

Given Board State {10D, 10C, JD, ?, ?} and 2 dead hands and one active hand, and your hand {JC, JS}:

Probability of other player holding two tens:

$2 over 43*42 $ = 0.11%, all the dead cards mean that 43 are remaining and there are 43P2 ways of choosing hands for that and only 2 in which the opposite player would have 2 10s.

River is Jack:

$frac{1}{41} + frac{1}{40}$ = 4.9%, either the first one is a Jack or the second one is a Jack

Dealt QD, probability of Royal Flush:

$frac{3P2*39}{41P3}$ = 14.6%, 3P2 ways to arrange the 2 cards you need and the other card you don't need over the possible ways you could be dealt the cards.

$frac{3P2}{39P2}$ = 0.6%, 3P2 ways to choose the jacks that you can have from 39P2 choices.

I apologize profusely because I am not very good at statistics and this has been troubling me greatly. I want to know the flaws in how I am thinking.