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Solutions_Activity_04

# Solutions_Activity_04 - ACTIVITY 4 Solutions 4.1 Situation...

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ACTIVITY 4 - Solutions 4.1 Situation: In 1998 the American Film Institute created a list of the top 100 American films ever made ( http://www.afi.com/tvevents/100years/movies.aspx ). Suppose that you and a date gather to watch one of these movies and, to avoid potentially endless debates about a selection, decide to choose a movie at random from the “top 100” list. You will investigate the probability that it has already been seen by at least you or your date. Let A denote the subset of these 100 films that you have seen, so the event A = {films that you have seen}. Similarly define event B for your date. The following 2x2 table classifies each movie according to whether it was seen by you and whether it was seen by your date. The “at random” selection implies that each of the 100 films is equally likely to be chosen; i.e., each has probability 1/100. Thus, the probabilities of these various events can be calculated by counting how many of the 100 films comprise the event of interest. Date Yes Date No Total You Yes 42 6 48 You No 17 35 52 Total 59 41 100 For example, the table reveals that 42 movies were seen by both you and your date, so P(A ∩ B) = 42/100 = 0.42 (read “the probability of A and B”). 1 a. Fill in the marginal totals of the table (the row and column totals). From these totals determine the probability that you have seen a randomly selected film and also the probability that your date has seen the film. (Remember that the film is chosen at random, so all 100 are equally likely.) Answer the following placing the proper event in the ( ). 2 P(You have seen it) = P( A ) = .48 P(Date has seen it) = P( B ) = .59 1 b. Translate the following events into set notation using the symbols A and B, complement, union, intersection. Also give the probability of the event as determined from the table above. Fill in the table below with these values. {If you cannot construct

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