Yes, Jessica is right. "Odds" is more related to mathematical, practical probability: my odds of winning are 5 to 1. The horse won against all the odds. (odds = probability) "Chance" is often used instead of "odds", but it's more related to divine intervention or pure casualty, more related to luck, or possibility: he never had a chance in life. I don't have any chance of winning the race! Opportunities is, as Jessica said, related to the possibility to achieve something. If in doubt on which word to use, use "chance". The odds of getting it right are higher! I hope you'll have the opportunity to use it, and that you take advantage of that chance.

Odds: this word could occur when debating the odds of something. For example: "The odds of me winning this game are slim." you could also use the word chances in that same case. The word opportunities could come up when discussing future goals or the opportunities you could receive in life. For example: "If I get this job my opportunities of getting a pay raise is good." I hope that helps or makes some sense.