TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. If n(A) = 14, n(A B) = 16, and n(B) = 7, then what is n(A ? B)?

2. If n(B) = 13, n(A B) = 30, and n(A ? B) = 4, find n(A).

3. A survey of 1500 subscribers to a certain news paper revealed that 1350 people subscribe to the daily morning edition and 750 subscribe to both the daily and the Sunday editions.

How many subscribe to the Sunday edition?

How many subscribe to the Sunday edition only?

1. In a survey of 200 members of a local sports club, 100 members indicated that they plan to attend the next Summer Olympic Games, 60 indicated that they plan to attend the next Winter Olympic Games, and 40 indicated that they plan to attend both games. How many members of the club plan to attend

(a) At least one of the two games?

(b) Exactly one of the games?

(c) The Summer Olympic Games only?

(d) None of the games?

1. In a survey of 400 households regarding ownership of HDTVs and DVD players, the following data were obtained.

345 households own one or more HDTVs.

180 households own one or more HDTVs and one or more DVD players.

15 households do not own an HDTV or a DVD player.

How many households only own one or more DVD players?

1. Data released by the Department of Education regarding the rate (percentage) of ninth-grade students who don't graduate showed the following results for the 50 states.

13 states had an increase in the dropout rate during the past 2 yr.

16 states had a dropout rate of at least 30% during the past 2 yr.

21 states had an increase in the dropout rate or a dropout rate of at least 30% during the past 2 yr.

(a) How many states had both a dropout rate of at least 30% and an increase in the dropout rate over the 2-yr period?

(b) How many states had a dropout rate that was less than 30% but that had increased over the 2-yr period?

1. Results of a Department of Education survey of SAT test scores in 22 states showed the following results.

9 states had an average composite test score of at least 1000 during the past 3 yr.

14 states had an increase of at least 10 points in the average composite score during the past 3 yr.

6 states had both an average composite SAT score of at least 1000 and showed an increase of at least 10 points during the past 3 yr.

(a) How many of the 22 states had composite scores of less than 1000 and showed an increase of at least 10 points over the 3-yr period?

(b) How many of the 22 states had composite scores of at least 1000 and did not show an increase of at least 10 points over the 3-yr period?

1. To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained.

132 students ate breakfast.

185 students ate lunch.

277 students ate dinner.

69 students ate breakfast and lunch.

112 students ate breakfast and dinner.

85 students ate lunch and dinner.

50 students ate all three meals.

How many students ate

(a) At least one meal in the cafeteria?

(b) Exactly one meal in the cafeteria?

(c) Only dinner in the cafeteria?

(d) Exactly two meals in the cafeteria?

1. In a survey of 400 individual investors regarding subscriptions to the New York Times (NYT), Wall Street Journal (WSJ), and USA Today (UST), the following data were obtained.

125 subscribe to the NYT.

155 subscribe to the WSJ.

66 subscribe to the UST.

37 subscribe to the NYT and WSJ.

29 subscribe to the WSJ and UST.

22 subscribe to the NYT and UST.

125 do not subscribe to any of these newspapers.

(a) How many of the individual investors surveyed subscribe to all three newspapers?

(b) How many subscribe to only one of these newspapers?