Question

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. If P​(​A)equals​0, then the probability of the complement of A is 1. C. If the probability of an event occurring is​ 1.5, then it is certain that event will occur. D. Probability can never be a negative value.

Answer 1

Answer:

C. If the probability of an event occurring is​ 1.5, then it is certain that the event will occur.

Step-by-step explanation:

Probability is a value between 0 and 1 (including both values). Thus, to say that there is a probability of 1.5 is not correct, and, therefore, this statement is not true.

We can rewrite the statement as "If the probability of an event occurring is 1, then it is completely certain that the event will occur."

Statement A.

Suppose the event is A. Then, if P(A) = 0, it is completely certain that the event will not occur. It is true.

Statement B.

$\\ if P(A) = 0\;then\;P(\overline{A}) = 1 - 0 = 1$. Then, the statement is true.

Statement C.

We already explained the statement C is not true because the values for probabilities are between 0 and 1 (including both values). A probability of 1.5 is meaningless as a result.

Statement D.

For the same reason explained in C, the probability can never be a negative value. So, this statement is also true.