Venn Diagrams & Two-Way Tables

Question

10) A student surveyed 226 classmates to see if they owned a dog or cat. There are 131 students who own a dog and 85 who own a cat. 34 students do not own a cat or a dog. Complete the Venn diagram by finding the value of b, c and d.

Use the diagram you completed in question 10 to answer questions 11-14. Leave your answer as a fraction in the lowest term.

11)What is the probability that a student chosen at random owns a cat?

12)What is the probability that a student chosen at random owns a cat, but not a dog?

13)What is the probability that a dog owner chosen at random does not own a cat?

14)What is the probability that a cat owner chosen at random also owns a dog?

Answer 1

P(D)= d/226 = 131/226

P(C)= c/226 = 85/226

P(D or C) = Pr(D) + Pr(C) - Pr(both C and D) =(c+d -b)/226 = 192/226

226 total

P(Neither C or D) = 34/226

P(D or C) = 1-34/226 = 192/226

192 = 131 + 85 - (b)

b=131+85-192=216-192 =24

b=24, c= 85, d= 131

Pr(C) = c/226 = 85/226

Pr(C, but not D) =(c-b)/226 = 61/226

Pr(D & not C/ D) =(d-b)/d = (107-24)/107 = 83/107

Pr(C & D /C) = b/c = 24/85

The Venn diagram is a rectangle with 2 overlapping circles inside

their overlapping portion = b = 24, the larger circle has 107 (c-b or 131-24), the smaller circle has 61 (d-b or 85-24). Outside the 2 circles but inside the rectangle = 34

34+107+24 + 61 = 226

the Venn diagram is divided into those 4 separate areas which add up to 226

34 who own neither

107 who own only dogs

24 who own both

61 who own only cats

add those number up to get the total 226