Question

Which of the following are the conditions to be satisfied in the axiomatic approach to probability?

• A. For any event E, P(E) $\ge$ 0
• B. P(S) = 1
• C. For two mutually exclusive events E and F, $P(E\cup F)=P\left(E\right)+P\left(F\right)$
• D. For two exhaustive events E and F, $P(E\cup F)=P\left(E\right)+P\left(F\right)$

Answer 1

Answer: (A), (B), (C)

For two mutually exclusive events E and F, $P(E\cup F)=P\left(E\right)+P\left(F\right)$

Even though axiomatic approach is a way of looking at problems in probability, the axioms are intuitive.

(a)$P\left(E\right)\ge 0$ . We know that probability of any event will be between 0 and 1, zero for impossible event (φ) and 1 for sample space S.

(b) $P\left(S\right)=1$

Probability of sample space is one, because if we conduct an experiment, the outcome will be one of the elements in sample space. That means the probability of sample space happening is one.
(c) We know from sets chapter that $E\cup F=E+F-E\cap F$
Similar result apply for probability, because we are actually counting the number of outcomes which favor our event
$\Rightarrow P(E\cup F)=P\left(E\right)+P\left(F\right)-P(E\cap F)$
For two mutually exclusive events $P(E\cap F)=0$
$\Rightarrow P(E\cup F)=P\left(E\right)+P\left(F\right)$

(d) The given result is applicable only if E and F are mutually exclusive