Here are the size of the two groups:
Group A = 246,940,000
Group B = 42,039,000
Occurrences:
Group A = 20
Group B = 22
How do I find out the probability difference between Group A and B?
Group B is smaller in size therefor the 22 occurrences should be much greater than that of Group A. I'm trying to find the percentage or rate (times) more likely they are from eachother. Thanks
Use units. Calculate per capita (Latin for "per person"). So for group A the per capita rate is $$ \frac{ 20 \text{ occurrences}}{246,940,000 \text{ people}} = 8.09913339 \times 10^{-8} \frac{ \text{occurrences}}{ \text{ person}} $$ or about 81 occurrences per billion people.
Make the same calculation for group B, and compare the result with that 81. Why should you expect the answer to be about six times as large?