Answer the following conceptual questions based on the axioms of probability.

MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability

Problem

Answer the following conceptual questions based on the axioms of probability. (a) Prove that

P(\varnothing)=0

for every probability function

P

defined on a sample space

S

. (b) Show that if

B\subseteq A\subseteq S

, then

P(B)\le P(A)

. (c) Give a brief explanation, using the axioms, of why a value such as

-0.2

cannot represent the probability of any event.