Using the total probability theorem, we calculate the likelihood of drawing a copper coin from either purse by adding the individual probabilities of choosing each purse and drawing a copper coin. The probability of selecting the first purse and then a copper coin from it is 1/2 multiplied by 4/7, which equals 4/14 or 16/56. The probability of selecting the second purse and drawing a copper coin is 1/2 multiplied by 6/8, which equals 6/16 or 3/8, equivalent to 21/56. Adding these two probabilities gives 16/56 plus 21/56, resulting in a final probability of 37/56.