Question

How many of the following are consistent with the axiomatic definition of probability ___
1) The probability of sample space is 1
2) P(A) belongs to the set [0,1] for any event A
3) $P(A\cup B)=P\left(A\right)+P\left(B\right)$ if A and B are mutually exclusive events

Answer 1

We know that the probability of a sure event is defined as 1 as per axiomatic approach. When a random experiment is conducted, any outcome is part of the sample space. It means sample space is a sure event. So its probability is 1. So the first statement is correct. Second axiom is that $0\le P\left(E\right)\le 1$ for any event E. In other words, 0 is the smallest allowable probability and 1 is the largest allowable probability.
$\Rightarrow$ second statement is true
We know that $P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(AB\right)$. If the events are mutually exclusive, then P(AB) = 0 .
$\Rightarrow$ Third statement is correct
​All the statements given are correct