The answer is dependent on the subtle nuance of how the question is asked. There are two possibilities: (a) the unconditional (*a priori*) probability that two randomly chosen tickets will have the same, winning outcome, and (b) the conditional probability that two randomly chosen tickets will have the same winning outcome *given that both tickets are winners*. "Winning" and "winners" here mean one of the outcomes that pays out a prize, not limited to the Jackpot.

Firstly, we need to recognize that there are two pools of balls. One has numbers 1 to 69, and the second has numbers 1 to 26. Five numbers are chosen at random from the first (main) pool, and one is chosen from the second (Powerball) pool. The total number of combinations is 292201338. To calculate the cases (a) and (b) described above we must first calculate the number of combinations that result in prize payouts.

Out of 292201338, there are a total of 11750538 that result in some payout ("winners"). Using the notation Main/Pball for (number of main balls matched) / (Powerball matched or not) here is the number of combinations breakdown for winning outcomes. "0" for Powerball means not matched, and "1" means matched.

0/1 = 7624512

1/1 = 3176880

2/1 = 416640

3/0 = 504000

3/1 = 20160

4/0 = 8000

4/1 = 320

5/0 = 25

5/1 = 1

Total = 11750538

To calculate the "unconditional" probability that two randomly and independently chosen tickets will have the same winning outcome, we need to square each possibility above and divide by the total number of combinations squared. Thus,

P(0/1; 2 winners) = 58133183238144 / 85381621928990200

P(1/1; 2 winners) = 10092566534400 / 85381621928990200

P(2/1; 2 winners) = 173588889600 / 85381621928990200

P(3/0; 2 winners) = 254016000000 / 85381621928990200

P(3/1; 2 winners) = 406425600 / 85381621928990200

P(4/0; 2 winners) = 64000000 / 85381621928990200

P(4/1; 2 winners) = 102400 / 85381621928990200

P(5/0; 2 winners) = 625 / 85381621928990200

P(5/1; 2 winners) = 1 / 85381621928990200

P(Total) = 68653825190770 / 85381621928990200 = **0.000804081998440691**

To calculate the conditional probability of the same winning outcome, given both tickets are winners, we take same numerators in the fractions above and instead divide by the square of 11750538, which is 138075143289444.

P(0/1 | Both are winners) = 0.421025695524941

P(1/1 | Both are winners) = 0.0730947388064133

P(2/1 | Both are winners) = 0.00125720593485903

P(3/0 | Both are winners) = 0.00183969390831999

P(3/1 | Both are winners) = 2.94351025331199E-06

P(4/0 | Both are winners) = 4.63515723940537E-07

P(4/1 | Both are winners) = 7.41625158304859E-10

P(5/0 | Both are winners) = 4.52652074160681E-12

P(5/1 | Both are winners) = 7.24243318657089E-15

P(Total | Both are winners) = **0.497220741946669**