This problem is also useful when done with manipulatives. The fact that the answers to the two problems are the same produces some cognitive conflict. Having students do the experiment repeatedly using both specifications, will lead to the recognition that 3/7 is indeed the probability in both cases. With this accomplished the principle seen by clicking on any of the choices can be explored and an understanding of the power of principles achieved. To augment this, students can suggest other changes consistent with the two corollaries and verify them by experiment.
The second case can also be solved using basic probability theorems. To see the solution to the second form of this problem click here.