| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
There are two parties, the blue party and the colorless party. There are 96 state seats, so you need 49 for a state majority. Federal seats consist of 16 state seats (demarcated by red borders in the above table). For a Federal majority, therefore, you need 4 seats.
In the above configuration, blue wins at the state level, while losing at the federal level.
The above configuration shows that the party holding the state majority need not win at the Federal level. The quality of victory at the state level matters - it is much better to win in a lot of federal level seats by a barely adequate margin, than to win very well in very few federal seats.
A concept by which state winning implies Federal winning is (stochastic) independence. If the state victories are independently distributed among federal seats, then the state victory will imply federal victory.
By the probability of victory of a party at the state level, we mean the fraction of seats which it wins. For the colorless party, it is 47/96 in this scenario.
For each federal seat, the probability of victory given that seat is the corresponding raction of winning seats inside that federal seat. For example, for the colorless party, it ranges from 3/4 to 0, depending on the federal seat.
If the distributions were independent, the probability of the colorless party in every federal seat would have been 47/96. This would mean that it loses every federal seat, hence the victorios party at the state and the federal level will be the same.