In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. you are going to select an individual from the group of students. the probability of event a is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. what is the probability of the event a’s complement?

Notice that 25+23+17+14+12+9=100, so among these students there are no 2 studying 2 subjects.

The probabilities of selecting students studying a certain subject are as follows

P(physics)=25/100
P(chemistry)=17/100
P(maths)=9/100

P(sociology)=23/100
P(political sciences)=14/100
P(anthropology)=12/100

since all the sets are disjoint, that is there are no common elements, and since all the students in consideration are enrolled in one these 6 subjects:

P(physics)+P(chemistry)+P(maths)+P(sociology)+P(political sciences)
+P(anthropology)=1

P(a)=P(sociology)+P(political sciences)+P(anthropology)+P(physics)

thus 

P(a')=1-P(a)=P(chemistry)+P(maths)=17/100+9/100=26/100=0.26

0.26