In bag 1, there are three marbles, a green, red and blue one. In bag 2, there is a red and blue marble, so it's impossible to win using both green. In bag one, you could say that two out of the three choices are needed to win and on the second bag, you need either blue or red to win. So two third times one halve is a one third possibility of wining.
After the experiment, it was in theory that he would win one out of the three times he picked marbles. So it would be 10 out of the 30 games. After the experiment, his results were only 1 win off. In theory, 10 of the games should of been won.