The shortest way to calculate it
The chance that your first chosen number is among the five main balls is 5/69. Once that number is in the result, the chance that your second chosen number is among the remaining four winning main-ball positions is 4/68.
5 / 69×4 / 68=20 / 4,692=1 / 234.6
So any particular pair — 1 + 2, 11 + 22, 31 + 69 or any other two distinct main numbers — has exactly the same chance of appearing together.
What happens after your pair appears?
There are then 67 other main numbers from which the remaining three winning main numbers can come. That creates 47,905 possible three-number sets:
C(67,3) = 47,905
There are also 26 possible Powerballs, so the number of complete pair-conditioned jackpot outcomes is 47,905 × 26 = 1,245,530.
How this reconnects to the full jackpot odds
Multiplying the chance of the pair appearing by the number of possible remaining main-number and Powerball outcomes takes you back to the standard Powerball jackpot odds:
234.6 × 1,245,530 = 292,201,338
That is why a pair wheel does not create an advantage over other distinct valid Powerball lines. It simply organises where your lines sit within the same overall outcome space.