Yes, it is not possible for you to be blood type B, if your parents are both blood type O. This is due to the manner in which your blood type is "passed on" from your parents.
An Austrian monk named Gregor Mendel first described how traits are passed on from one generation to another in 1866.
Each child receives an A, B, or O gene from each parent. The A and B genes are co-dominant and the O gene is recessive.
Thus, a person whose genetic type is either AA or AO will have blood type A. Those with genetic type BB or BO will have blood type B.
If your blood type is O, it follows that your genetic type will be OO.
Hence, all the children of parents who are blood type O, will be blood type O as well.
It is not possible to carry out the test without your parents knowing, as any paternity test will require DNA material (buccal cheek swab, or blood sample) from both your mom and your dad.
All legal DNA tests also require a consent signature from the person whose samples were submitted. So if you want to do a legal paternity test, it cannot be secret or hidden from your parents.
The Health Sciences Authority performs paternity tests in Singapore. There are also a few private companies now offering cheaper paternity tests, ranging from $600 to $700.
Hope that helps!
