Multiple choice questions. A teacher is preparing test papers in multiple choice format. Each question has four choices—A, B, C, and D. After the exam, the teacher recorded the number of students who selected each of the choices as shown in the following table. Are each of the following probabilities possible? Why?

Probabilities of …
A B C D

a) 0.1 0.3 0.3 0.4

b) 0.5 0.5 0 0

c) 0.45 0.15 0.35 0.05

d) 0 -1 0 0

e) 0.2 0.1 0.3 0.2