odds ratio question

I have the following data:

Group A starting in Jan.: Pass: 40, Fail: 60
Group B starting in Feb.: Pass: 90, Fail: 50
Group C starting in Mar.: Pass: 100, Fail: 70

I want to know if Group A has a lower pass rate than the overall population(Group A+B+C).

Does it make sense just to test the following 2x2 table?

Group A starting in Jan.: Pass: 40, Fail 60
Group A+B+C : Pass: 230, Fail 180
Most tests try to conclude as the whether populations are different. So - I think you should take group A out of the second category to allow mtually exclusive groups. This will give you: A vs B+C.