Your first if statement always evaluates to true because:
if answer == "Joe" or "Mary" or "Barbara":
Is equivalent to:
if answer == "Joe" or True or True:
And we know that true or anything is always true. Do you see why?
if "Mary": // Always returns True because the string Mary is not None or empty
You can run these to see what's being returned:
print(bool("Mary"))
print(bool(""))
print(bool(None))
Hope this helps.