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4 years ago

VENN DIAGRAMS HELP?

Mathematics

1 answer:

user100 [1]4 years ago

7 0

Answer:

a. Probability of student having both cat and dog = 9/25

b. Probability of student not in drama club or sports team = 105/330

c. Probability of student who play both cricket and football = 10/32

Step-by-step explanation:

a. Given,

Total Students = 25

A = Students with cat = 15

B = Students with dog = 16

Students with both dog and cat = A∩B

A∪B = Total students - Students with neither dor or cat = 25-3 =22

A∪B = A + B - A∩B

A∩B = A + B - A∪B

A∩B = 15 + 16 - 22 = 9

Hence probability (A∩B) = A∩B÷Total Students = 9/25

b. Given,

Total Students = 330

A = Students with in drama club = 85

B = Students with in sports team = 200

Students in both drama and sports team = A∩B = 60

A∪B = Total students - Students in neither in drama or sports

A∪B = A + B - A∩B

A∪B = 85 + 200 - 60 = 225

A∪B =300 - Students in neither in drama or sports

Students in neither in drama or sports = 300 - 225 = 105

Hence probability (Students in neither in drama or sports) = Students in neither in drama or sports/Total Students = 105/330

c. Given,

Total Students =

A = Students playing football = 14

B = Students playing cricket = 21

Students playing both football and cricket = A∩B = 10

A∪B = Total students - Students playing neither football or cricket

A∪B = A + B - A∩B

A∪B = 14 + 21 - 10 = 25

A∪B = Total students - Students playing neither football or cricket

A∪B = Total students - 7

Total students = 25 + 7 = 32

Hence probability (A∩B) = A∩B÷Total Students = 10/32

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