Board Thread:General Discussion/@comment-26907577-20191002153041/@comment-26907577-20191113142610

Where are you getting 25%? You want probability? Read the OP.

Time for a math lesson. P = H - S That is the fewest possible pairs. What if you had seven colors, but two humans? Then you get. But you could have them both be cyan! In fact, there's a 1 in S chance that any two humans have the same SOUL color. And if we have more than two humans total, then we need to try this with all the combinations.

With Alice (she), Bob (he), and Chara (they), and SOUL colors Orange, Yellow, Green, Cyan, Blue, Purple, Red , we have some math to do.

Alice has a  chance of sharing a SOUL color with Human 0, because there is no Human 0.

Bob has a  chance of sharing a SOUL color with Alice.

Chara has a  chance of Bob not sharing a SOUL color with Alice, in which case they have a   chance of sharing a SOUL color with one of the first two. 6/7 * 2/7 = 12/49.

Chara has a  chance of Bob sharing a SOUL color with Alice, in which case they have a   chance of sharing a SOUL color with both of them. 1/7 * 1/7 = 1/49.

So, Chara has a  chance of sharing a SOUL color with Alice or Bob.

Now, what're the odds that there's exactly one match?

If Bob shares a SOUL color with Alice, then we want there not to be another match. The odds of Chara not sharing a SOUL color with both of them is an additional. 6/7 * 1/7 = 6/49.

If Bob doesn't share a SOUL color with Alice, then we want there to be a match between Chara and one of them. The odds of that are. 2/7 * 6/7 = 12/49.

12/49 + 6/49 = 18/49. That's about 36.7%. With only three humans. And discounting the option where they all match (An additional, for 38.8%).

There are formalized mathematical operations (see OP) that let us figure out the odds without considering each pair individually. But this is just breaking it down, to see how it works. See also the Birthday Problem on Wikipedia; for  and   of only , a 50% chance of at least one match.

Does that make sense?