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∪B)=P(A)+P(B) if A and B are mutually exclusive events
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∪B)=P(A)+P(B) if A and B are mutually exclusive events
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≤P(E)≤1 for any event E. In other words, 0 is the smallest allowable probability and 1 is the largest allowable probability.
⇒ second statement is true
We know that P(A∪B)=P(A)+P(B)−P(A∩B). If the events are mutually exclusive, then P(A∩B)=0 .
⇒ Third statement is correct
All the statements given are correct
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≤P(E)≤1 for any event E. In other words, 0 is the smallest allowable probability and 1 is the largest allowable probability.
⇒ second statement is true
We know that P(A∪B)=P(A)+P(B)−P(A∩B). If the events are mutually exclusive, then P(A∩B)=0 .
⇒ Third statement is correct
All the statements given are correct
