I recently saw a math video in the online edition of a Spanish divulgation magazine. In the video, they had three boxes, one yellow, one red and one blue. A 1,000,000€ check was put inside one of the boxes and then a girl was asked to choose one of the boxes. She chose the red box, and then the host opened the yellow one that was empty. He then asked the girl if she wanted to change her mind and choose the blue box. He, then, said that changing the box was the correct answer, because at the start, the red box had 1/3 of being the correct box, and the yellow or blue had 2/3, and after opening the yellow one this was still 2/3, so it was more probable that the blue box was correct.
This strikes me as a statistical fallacy, but I'm not sure. Am I right or is there something here I can't understand?