I am on the last day of my menstrual cycle. what is the probability of the average female becoming pregnant after sex at this time ?

Low probability.: Assuming normal regular menstrual cycles (menses usually last from 3-7 days), it's unlikely ovulation will occur by the end of the menses or within 3 days of cessation of the menses (sperm can survive for 3 days inside the vagina). Ovulation usually occurs at the end of the follicular phase (usual length 14-21 days, counting the first day of the menses as day #1, depending on your cycle length)