Question

In order to ensure the safety of school classroom, 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. 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)