KöMaL 2019 B5007

We have $3n+1$ coins, $n$ of which have 0 on one side and $11$ on the other. Another $n$ coins have 0 on one side and $44$ on the other, and the remaining $n+1$ coins have 0 on one side and $99$ on the other. All the coins are tossed at the same time. What is the probability that the sum of the resulting numbers is divisible by 7? (The coins are fair coins.)