Does the liklihood of pregnancy increase from starting a new birth control pack 1 day late? sex last day of period. ovulate after missing 1 pill?

Possible: While highly unlikely, it is possible to ovulate in the first week of your pill pack, so it's important to try never to miss pills that first week. Having said that, the likelihood is still very low given unlikely to ovulate that early in one's cycle. I would continue your pills through end of pack and then check a pregnancy test at end of pack.