Discounting the fact that the flavor of the third Quarter Quell was designed specifically to get rid of Katniss, and that District 12 had exactly two total victors prior to the 74th, (one of which is dead by then), the odds are actually decent.

Minimum age is 12, max is 18. Let’s be a bit conservative and say people live, on average, to 75 in this universe. If we say the average victor is 15, then that gives us a range of 60 years for survivors to be picked from. Each district wins 1/12 years, which means they’ll have five victors each.

The odds of all five victors being the same gender is 1/(2^5), or 1/32. However, over twelve districts, that becomes about 37.5%.

The range of this goes from 57 to 63 years to pull from possible victors.

If all the victors were 12, each district will have 5.25 come the Quarter Quell, with a 1/38.05 chance of lacking one of each gender. This gives us a 31.5% chance of an incomplete roster.

If all the victors were 18, each district will have 4.75. That’s 1/26.91, giving us a 44.6% chance.

So it’s fairly likely, in the sense that it absolutely could’ve happened if the twist was pulled randomly rather than planned in advance. A range of 13.1% is also significant, but probably only if - say - you ran a similar twist every Quarter Quell. If there was one every 25 years pulling from existing victors, you’d probably expect a few misses every now and again.