Slight, but possible. If you ovulate close to a period, you could get pregnant, but sometimes people are pregnant anyway - and unaware of it, because you can still have a loss of blood during this time. An old lady I know swears that she had periods for 8 months of her pregnancy. When they stopped, she went along to the doctors, hoping to be pregnant with her first child. The shock of hearing that she was pretty close to having him was enough to make it happen there and then!