BHS Statistics
August 20, 1999

Investigating "Unusualness"

The idea of "unusual" that we will investigate is this: An event is "unusual", or "unlikely", or "rare" if over the long run we expect to see it a small fraction of the time. This way of thinking about unusualness does not say anything about the event per se. Rather, it emphasizes our expectation that, for whatever reason and relative to certain circumstances, we expect to see it relatively infrequently.

In that light, look at these situations and plan an investigation of the events' "unusualness". Begin your investigations by first saying what you must reasonably assume about the situation to allow you to investigate it. Then, describe the overall strategy you will use and how you will use ProbSim to carry it out.

1. Jill was in a class of 25 people. The teacher asked each student for his or her birthday to enter in the class calendar. The class was surprised when two people had the same birthday! Is this, in fact, an unusual event?

Strategy/method of investigation:

Result:

Conclusion:

2. Ayako, Allyson, and Epsilon selected 5 candies at random from a bag holding 216 red candies and 216 white candies, and they repeated this process 10 times. Here are their results:

 No. reds 0 1 2 3 4 5 No. Samples 0 5 2 1 0 1

Question: Does this set of results suggest that, unbeknownst to them, their process of selecting samples introduced a bias toward picking fewer reds than whites?

Strategy/method of Investigation:

Result:

Conclusion:

3. Ephram works at a theater, taking tickets for one movie per night at a theater that holds 250 people. The town has 30 000 people. He estimates that he knows 300 of them by name.

Ephram noticed that he often saw at least two people he knew. Is it in fact unusual that at least two people Ephram knows attend the movie he shows, or could people be coming because he is there? (The theater holds 250 people.)

Strategy/method of Investigation:

Result:

Conclusion: