Good ol' Matthias.
He's apparently been part of a group of people who followed Jesus, although not one of the 12, and he's now brought forward as a candidate for that circle to replace Judas. The lots are cast, Matthias is named, and we never hear from him or about him again. Not anything for certain anyway.
Church tradition says that Matthias preached the gospel in an ancient area called Aethiopia, which is not the Ethiopia we know as a country today but a region in what is now Georgia. Not Rhett Butler Georgia, although the misnaming of the area might lead one to wonder whether some of the folks in the ancient world were any better at geography than those people we read about who keep failing geography tests.
Matthias was supposed to have been crucified there, although we have this only from some church traditions and we can't verify it by any of the New Testament or the better-known writings of the early church.
He was chosen through the process called "drawing lots," or sometimes "casting lots." We don't know exactly what this was. We know that it was a way of making a random choice, and that it was probably made up of pieces of wood or stone that had different colors or symbols on each side. When they were thrown, some would come up one way and some another, and the outcome of the decision would be made according to how many came up a certain way.
In other words, Matthias was chosen by the apostles shooting dice, which would have come as a surprise to my dice-avoiding, card-shunning grandparents.
Before deciding between the two men, Matthias and Joseph Barsabbas, the disciples prayed and sought the guidance of the Lord. Then they cast the lots. The idea was that since the lots fell in a completely random way, there was no possibility of human influence on the choice, and they could be confident God alone was involved.
Now, you might think they would have been more careful. After all, they're replacing the one member of their circle who betrayed Jesus, which is the kind of PR wrinkle you'd like to avoid bringing attention to. So perhaps we would have advised them to look for an "anti-Judas," and have a rigorous screening process.
But what screening process would have been better than Jesus' own perceptions? If Jesus couldn't guarantee a fault-free choice, what makes them think that they ever could? And Judas wasn't the only disciple who "failed" Jesus, either. Remember that Peter denied him and the rest abandoned him. So our instinct to rely on our judgment might not work so well, and they used the method that was most likely in their minds to follow God's will for them.
Perhaps the main reason was the understanding that if God was at work, then either man would be the right choice. If God was at work, then he would use Matthias, if Matthias let himself be open to that. If God was at work, then he would have used Joseph Barsabbas just as well. We know that even though we never really hear about Matthias again, he must have done something (along with the other apostles), because the gospel was proclaimed throughout the old Roman Empire and beyond.
It takes trust in God to bring someone in to help with his work, because we don't know if those people will do it the right way (or, if we're being honest, "our way") and we don't know if there will be problems or not. Or if those problems can be handled. Or if things will be the same. Since we don't know, we must trust.
The disciples trusted God to lead them to Matthias, and then trusted Matthias to do God's work in the way that best suited him and best followed God. That.s a pretty good example.