Question

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?

Answer 1

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


Answer: 0.26