SUGGESTED ANSWER TO QUESTION 1-1(b)

Lottery numbers are chosen at random, typically once a week in many states. One week, the following five winning numbers were drawn in a certain state: 12, 32, 4, 78, and 63. A week later, the same five numbers were again drawn in this state.

In the following, two possible explanations are mentioned. You may have thought of other possibilities.

One possible explanation is that there was some failure of the randomization process, perhaps caused by some fraudulent activity. Another possible explanation is coincidence: we would expect, given the many tens of thousands of times that lottery numbers have been chosen over the years, that eventually the same numbers would be picked twice in a row.