Questions: Which of the following statements is not true? A. If the probability of an event occurring is 0, then it is impossible for that event to occur. B. An event can have a probability of 1.5 of occurring. C. If P(A)=0, then the probability of the complement of A is 1. D. Probability can never be a negative value.

Solution Steps

To determine which statement is not true, we need to evaluate each statement based on the fundamental properties of probability. A probability value must be between 0 and 1, inclusive. Therefore, any statement suggesting a probability outside this range is false.

Statement A claims that if the probability of an event occurring is \( P(A) = 0 \), then it is impossible for that event to occur. This is true because a probability of \( 0 \) indicates that the event cannot happen.

Statement B states that an event can have a probability of \( 1.5 \) of occurring. This is false because the probability of any event must lie within the range \( [0, 1] \). Therefore, \( P(A) = 1.5 \) is not a valid probability.

Statement C asserts that if \( P(A) = 0 \), then the probability of the complement of \( A \), denoted as \( P(A') \), is \( 1 \). This is true because the sum of the probabilities of an event and its complement must equal \( 1 \): \[ P(A) + P(A') = 1 \implies 0 + P(A') = 1 \implies P(A') = 1. \]

Statement D claims that probability can never be a negative value. This is true, as probabilities are defined to be within the range \( [0, 1] \).

Final Answer