In this lab you are going to estimate the value of based on probability ratios. You will be given a target paper with five circles inscribed within five squares. Using a centimeter ruler you are first to measure the length of each square and record your answers to two-decimal places in the data table below.
Next completely cover your target paper with a piece of carbon paper, placing it inky-side down. Now drop a marble 100 times onto the carbon paper. Make sure that you randomly release the marble so that each part of the paper receives relatively the same number of impacts. When you are finished, count the number of hits that are totally within each circle. Do NOT count a hit that lies on the edge of a circle. Next count the total number of hits that lie completely within each square - including the hits on the edge of the circle, within the circle, and in the area between the circle and the square. Do NOT count the hits that fall on the edge of the square. Record your answers in the data table below. The left picture represents the hits landing on one circle/square. On the right picture, the dots which need to be discarded have been marked. Dots circled on the edge of the circle count for the square but not for the circle. Dots on the end of square do not count anywhere. Obviously, any dots that fell outside of the square were not counted. number of dots in the circle = 39 number of dots in the square = 39 + 15 = 54 the ratio of hits would be: 39/54 = 0.722 or 72.2% Data table: |