Chances of pregnancy close to your periods are minimum but exist. Because under the normal conditions, egg is dead close to the periods, that is why periods start. This is possible if ovulation takes place at mid of the cycle. Chances of pregnancy close to periods rely on the ovulation. In some ladies, ovulation occurs late. Sex 3-4 days before and 10-12 hours after ovulation can result in to pregnancy and periods will not start on due dates. Life of the egg is 24 hours after ovulation and during this periods fertilization is possible and periods start if there is no conception.