Probability is the possibility of an event occurring. In this case the marbles are chosen without replacement, therefore the total number of marbles decreases every time a marble is chosen.
The possible outcomes are RG, RR, RB, GG, GR, GB, BB, BG, BR. Thus those that contain different colors are RG,RB,GR,GB,BG,BR
calculation will be (10/37×15/36) +(10/37 × 12/36) + (15/37 ×10/36) + (15/37×12/36) + (12/37 ×15/36) +(12/37×10/36) = 25/37.
Therefore, the probability of choosing different colors (without replacement) is 25/37.