In the final stages of a patient's immune response is severely diminished.
a. the common cold
b. aids
c. smallpox
d. cancer

The common cold is not the answer.

Reason:
Colds last at least for 2-3 days and is harmless. The symptoms, which is sneezing, coughing, etc... happens because it releases the bacteria that has entered the body. A patient with a common cold will actually have an improved immune system because its defensing skills improve. 

Smallpox is not the answer.

Reason:
Smallpox, just like chickenpox, doesn't harm the immunity that much. Instead, the skin is mostly irritated and people could survive it.

Cancer and AIDS both do severely effect the patient but AIDS effects the Immunity more.

AIDS: Stands for Acquired Immune Deficiency Syndrome. The name explains it. It severely damages the immune system at its final stage and may end up killing the patient. 

However, Cancer is slowly passed to the other organs which weakens the immune system but the answer you are looking for is AIDS. (B)

Hope I helped. :)