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
