I started a new pack of birth control a week late and had unprotected sex the day before i started a new pack. what are my chances of getting pregnant?

BCP/a week late: If you were on birth control pills before the "week late" ( i.e., a week after the last of the placebo pills were finished), since placebos are seven days, adding a week and having sex is no different than having unprotected sex without bcp, i.e., you could certainly become pregnant. Stop the bcp and wait a couple weeks ( the pills won't help at this point anyway), then get a serum HCG test.

Good & bad news: First the bad news, the delay in re-starting your oral contraceptive may have allowed early ovulation to occur which means that conception is slightly possible. The good news is that the resumption of the pill will make the endometrium (lining of the womb) inhospitable for implantation, again, making conception less likely.