Solving Problems Involving Union and Intersection of Two Events Using Venn Diagram

In this topic, we have to define first Cardinality as it is very much involved.

Cardinality

The number of elements in a given event. It is denoted by the symbol n. "Cardinality of event A" is written as n(A).

Sample Problems:

1. Forty people are asked about the social media accounts that they have. How many people have:

a. Facebook or Instagram accounts?

n (FUI) = 8 + 7 + 5 + 2 + 4 + 3

n (FUl) = 29

b. Twitter and Instagram accounts? 

n (Tnl) = 2 + 4

n (Tnl) = 6

c. Facebook or Twitter accounts?

n(FUT)= 8 + 7+ 5 +2+ 4 + 6

n(FUT)= 32

2. A health worker surveyed 100 patients in a quarantine facility to find out how many patient experience the symptoms of COVID - 19. 31 patientsvhave high fever, 26 patients have dry cough, land 12 patients experience both symptoms. Draw the Venn diagram for the ff:

a. Patients who have high fever or dry cough.

b. Patients who have dry cough only .

c. Patients who only have one symptom.

d. Patients who are asymptomatic.

100 - (19 + 12+ 14) = 55

3. Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in both classes, how many students are in neither class?

4. In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. How many students in enrolled in either Chorus or Band?

5. In a class there are: 8 students who play football and hockey, 7 students who do not play football or hockey, 13 students who play hockey, 19 students who playbfootball. How many students are there in the class?

6. In a class there are 30 students. 21 students like Math, 16 students like English, 6 students don't like Math or English. How many students like both math and English?

n(MnE) = n(M) + n(E) - n(MnE) 

= 21+ 16–24

=13

7. A veterinarian surveys 26 of his patrons. He discovers that 14 have

dogs, 10 have cats, and 5 have fish. 

Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?

= 26 - (7 + 4 + 5 + 1 + 1 + 3)

=5