Question

In order to ensure the safety of school classrooms the local Fire Marshall does an inspection at Thomas Jefferson High School every month, looking for faulty wiring, overloaded circuits, etc. At TJHS the new Academic Wing has 5 math rooms, 10 science rooms, and 10 English rooms. The science rooms are divided into 8 biology and 2 chemistry rooms. Each month, the Fire Marshall randomly picks one of the rooms in the new wing to inspect each month. Define the following events:
S = the event the selected room is a science room
B = the event the selected room is a biology room
M = the event the selected room is a math room
E = the event the selected room is an English room
C = the event the selected room is a chemistry room
Calculate the probabilities of the events described below:
a) P(S) b) P(M or E) c) P(E or B) d) P(S and not C)

Answer 1

The probability of each is the fraction of that item (or group of items) to the total. They just tried to trick you by listing Science with subcategories of biology and chemistry to see if you would add them twice and get the wrong total. Total rooms is M+S+E=5+10+10=25 
S=10/25 
B=8/25 
M=5/25 
E=10/25 
C=2/25 

For the "or" questions you just add them. P(MorE) = P(M) = P(E). 
For S and not C that's just B.

I hope my answer has come to your help. God bless and have a nice day ahead!