Chapter 7 Sets & Probability Section 7.2 Applications of Venn Diagrams

Shade the region corresponding to A   B .

Shade the region corresponding to A   B . Step 1: Shade the region corresponding to A . A B

Shade the region corresponding to A   B . Step 2: Shade the region corresponding to B . A B The intersection of A   B is the overlapping region that has been shaded twice.

Shade the region corresponding to A   B .

Use a Venn diagram to shade in the region corresponding to the indicated set. a.) B  A b.) B   (A  C ) c.) A  (B  C) 

A survey of 200 people yielded the following information: 94 owned a VCR, 127 owned a microwave oven, and 78 owned both. How many people owned the following? a.) a VCR or a microwave oven b.) a VCR but not a microwave c.) a microwave oven but not a VCR d.) neither a VCR nor a microwave oven

A survey of 200 people yielded the following information: 94 owned a VCR, 127 owned a microwave oven, and 78 owned both. n(U) = 200 n(V) = 94 n(M) = 127 n(V  M) = 78 V M 16 78 49 57

A survey of 200 people yielded the following information: 94 owned a VCR, 127 owned a microwave oven, and 78 owned both. How many people owned… a.) a VCR or microwave oven? n (V  M) = 16 + 78 + 49 = 143 b.) a VCR, but not a microwave oven? n (V  M) = 16 c.) a microwave oven, but not a VCR? n (M  V) = 49 d.) neither a VCR nor a microwave oven? n (M  V) = 57 V M 16 78 49 57

The records of 1492 high school graduates were examined, and the following information was obtained: 1072 took biology, and 679 took geometry. If 271 of those who took geometry did not take biology, how many graduates took the following? a.) both classes b.) at least one of the classes c.) biology but not geometry d.) neither class

In a survey, 674 adults were asked what television programs they had recently watched. The following information was obtained: 226 watched neither the Big Game nor the New Movie, and 289 watched the New Movie. If 183 of those who watched the New Movie did not watch the Big Game, how many of the surveyed adults watched the following? a.) both programs b.) at least one program c.) the Big Game d.) the Big Game but not the New Movie

Recently, U2, Sting, and Lollapalooza each toured the United States Recently, U2, Sting, and Lollapalooza each toured the United States. A large group of college students was surveyed, and the following information was obtained: 1533 saw U2, 1127 saw Sting, 581 saw Lollapalooza, 219 saw all three, 1853 saw none, 766 saw only U2, 654 saw U2 and Sting, and 92 saw Sting and Lollapalooza but not U2. a.) What percent of the college students saw all three acts? b.) What percent of the college students saw at least two of the acts?

A kindergarten teacher wants to do an activity about common household pets. She begins the activity by asking her class the following questions and records the children’s answers. “How many of you have a dog?” 15 “How many of you have a cat?” 10 “How many of you have both?” 7 How many of the children had a dog or a cat?

Union Rule for Sets (General Rule) n(A  B) = n(A) + n(B) – n(A  B) n(D) = 15 n(C) = 10 n(D  C) = 7 n(D  C) = n(D) + n(C) – n(D  C) n(D  C) = 15 + 10 – 7 n(D  C) = 18

Union Rule for Disjoint Sets n(A  B) = n(A) + n(B) Note: Use this rule only when the two sets do not have any elements in common. To be on the safe side, you can always use the General Union Rule for Sets.

A company that specializes in language tutoring lists the following information concerning its English-speaking employees: 23 speak German, 25 speak French, 31 speak Spanish, 43 speak Spanish or French, 38 speak French or German, 46 speak German or Spanish, 8 speak Spanish, French, and German, and 7 office workers and secretaries speak English only. a.) What percent of the employees speak at least one language other than English? b.) What percent of the employees speak at least two languages other than English?