Which of the following is NOT true with respect to the properties of probability?
0 < x < 1
P(S) = 1, where S is the sample space
P(A) + P(Ac) = 0
If two events are independent then P(A and B) = P(A) * P(B)
P(A) + P(Ac) = 0
p(A)+p(Ac)=0
The statement "P(A) + P(Ac) = 0" is NOT true with respect to the properties of probability.
To determine which statement is NOT true with respect to the properties of probability, we will analyze each statement individually.
1. 0 < x < 1
This statement is a general property of probability. The probability of an event always falls between 0 and 1, inclusive. Therefore, this statement is true.
2. P(S) = 1, where S is the sample space
In probability theory, the sample space refers to the set of all possible outcomes of an experiment. The probability of the entire sample space is always equal to 1, as one of the outcomes must occur. Therefore, this statement is also true.
3. P(A) + P(Ac) = 0
Here, A represents an event, and Ac represents the complement of A (the event that A does not occur). The sum of the probabilities of an event and its complement is always equal to 1, not 0. This statement is incorrect.
4. If two events are independent then P(A and B) = P(A) * P(B)
This statement represents the multiplication rule for independent events. If two events, A and B, are independent, the probability of both events occurring can be calculated by multiplying the probabilities of each event occurring individually. Therefore, this statement is true.
In conclusion, statement 3 is NOT true with respect to the properties of probability.