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

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Solution

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 $0 \leq P (E) \leq 1$ 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 $P (A \cup B) = P (A) + P (B) - P (A B)$ . If the events are mutually exclusive, then P(AB) = 0 .
$\Rightarrow$ Third statement is correct.
All the statements given are correct.

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