A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffine mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the selected will be one who purchases neither cake mix nor muffine mix?
For these kind of problems, I would rather make a Venn diagram and solve for the unknown quantity. This is a great question in which both concepts are tested i.e. usage of Venn diagrams and probability.