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)
To determine which of the statements is NOT true, let's analyze each statement one by one:
1. 0 < x < 1: This statement is a basic property of probability. It states that the probability of an event always lies between 0 and 1, exclusive (0 < P(A) < 1). This statement is true.
2. P(S) = 1, where S is the sample space: This statement is also one of the fundamental properties of probability. The probability of the sample space, which includes all possible outcomes, is always equal to 1. This statement is true.
3. P(A) + P(A') = 0: This statement claims that the sum of the probability of event A and its complement, A', is equal to 0. However, this statement is NOT true. The sum of the probability of an event and its complement is always equal to 1 (P(A) + P(A') = 1), not 0.
4. If two events are independent, then P(A and B) = P(A) * P(B): This statement is known as the multiplication rule for independent events. It states that if two events are independent, the probability of both events occurring is equal to the product of their individual probabilities. This statement is true.
Therefore, the statement that is NOT true with respect to the properties of probability is:
3. P(A) + P(A') = 0, since it contradicts the actual property of probability (the correct statement is P(A) + P(A') = 1).