Investigation 1: Matching Cell Phones (due Thur, Sept 23)
You may work with one other person on this, handing in
one report with both names.
Word-processed reports are preferred to hand-written ones.
Reconsider the "matching problem" that you investigated through the "random babies" activity.
Suppose that three executives (Bob, Jay, Mary) drop their cell phones in an elevator and that each then picks up a cell phone at random.
a) List the sample space of possible outcomes of this process.
b) Use the sample space to determine the probability that everyone gets the right phone, the probability that noone gets the right phone, and the probability that exactly one person gets the right phone.
c) Determine the expected value of the number of people who get the right phone.
Now suppose that there are five executives rather than three.
d) How many outcomes comprise the sample space? [Do not bother to list them.] What is the probability that all five would get the correct phone?
e) Since it's cumbersome to list the outcomes in this sample space, simulation can be very helpful for approximating probabilities. Simulate 1000 repetitions of this process (again with the applet), and report empirical estimates of the probability of zero, one, two, three, four, and five matches. Also report an empirical estimate of the long-term average number of matches.
Finally, suppose that there are eight executives.
f) How many outcomes comprise the sample space? [Do not bother to list them.] What is the probability that all eight would get the correct phone?
g) Since it's unreasonable to list the outcomes in this sample space, simulate 1000 repetitions of this process (again with the applet), and report empirical estimates of the probability of zero, one, two, three, four, five, six, seven, and eight matches. Also report an empirical estimate of the long-term average number of matches.
h) What happens to the probability of everyone getting the right phone as
the sample size increases from