Social Friends

Mutually  & Non Mutually Exclusive Events

Kelvin and Cynthia have their own groups of friends at St. Brother Andre. Some of Kelvin’s friends are friends with Cynthia. Same goes with some of Cynthia’s friends, they are friends with Kelvin. However, Cynthia also has friends from work and Kelvin doesn’t have any work friends because he doesn’t have a job. We can say Cynthia’s work friends are mutually exclusive to Kelvin and his friends because they have never met one another and do not have a connection. Conversely, the friends that are common with both Cynthia and Kelvin are considered to be non-mutually exclusive events. In total Cynthia has 308 friends, 41 from work and Kelvin has 84 friends. Kelvin and Cynthia found that the total number friends they have in common are 33.

Additive Principle:
Answer: The example gives 2 sets (# of Cynthia's friends and # of Kelvin's friends). The number of elements in A∪B can be found by adding the total of number of elements in both sets and subtracting the elements that have been counted twice (A∩B).

Kelvin and Cynthia decided to figure out the number of friends that are friends with Kelvin or with Cynthia.  

                          

A = # of friends Kelvin has

B = # of friends Cynthia has

n (A ∪ B) = n (A) + n(B) – n(A ∩B)

                 = 84 + 308 – 33

                 = 359

 ∴ 359 is the number of friends that are friends with either Kelvin or Cynthia.