Investigation 3: Top 100 Films (due Wednesday, September 29)

You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are preferred to hand-written ones.

a) Work with a partner (who may or may not be a student in this class) to look through the American Film Institute’s Top 100 list of American films (www.afi.com/tvevents/100years/movies.aspx). Keep track of which movies you have seen and which your partner has seen. Create a two-way table to display these counts.

Suppose that one of these 100 films is chosen at random.

b) What is the probability that you have seen the film? What is the probability that your partner has seen it?

c) What is the conditional probability that you have seen the film, given that your partner has seen it? How does this compare to the (unconditional) probability that you have seen the film?

d) What is the conditional probability that you have not seen the film, given that your partner has not seen it? How does this compare to the (unconditional) probability that you have not seen the film?

An event A is said to carry positive information about an event B if P(B|A)>P(B). An event A is said to carry negative information about an event B if P(B|A)<P(B).

e) Does the event that your partner has seen the film carry positive or negative information (or neither) about the event that you have seen the film? Explain.

f) Construct a hypothetical two-way table for two people (call them Siskel and Ebert) so that Siskel’s having seen the film carries negative information about Ebert’s having seen the film. Show calculations to demonstrate the negative information.

g) Consider two generic events A and B. Show that if A carries positive information about B, then B must carry positive information about A. Explain every step in your argument.