There are sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes a random sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that .
Not a difficult question. I would lengthen the last sentence to read: Use this information to show that must satisfy the following equation. But a pointless one. It gives the study of mathematics a bad name. How is it we know there are only two colors of sweets in the bag without knowing ? How is it we know that there are only 6 orange sweets without knowing how many yellow ones there are? Why can’t I work out by emptying the bag and counting its contents? In short, students are asked to accept an implausible premise to compute something that can be done simply by other means.