Which of the following is NOT a principle of probability? Choose the correct answer below:
A. The probability of an impossible event is 0.
B. The probability of an event that is certain to occur is 1.
C. The probability of any event is between 0 and 1 inclusive.
D. All events are equally likely in any probability procedure.
The Correct Answer is Explanation
The correct answer is D. All events are equally likely in any probability procedure.
Explanation:
In probability theory, there are several key principles that govern the likelihood of events happening. Let’s break down each option to understand why D is the correct answer:
- A. The probability of an impossible event is 0.
- This is a fundamental principle of probability. If an event cannot possibly occur, such as drawing a red card from a deck of only black cards, the probability of that event is 0. Probability ranges from 0 (impossible event) to 1 (certain event).
- B. The probability of an event that is certain to occur is 1.
- This is another core principle. If an event is certain to happen, such as rolling a number between 1 and 6 on a standard die, the probability is 1. Probability ranges between 0 and 1, and 1 represents certainty.
- C. The probability of any event is between 0 and 1 inclusive.
- This is a basic and true rule in probability. The probability of any event must be a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
- D. All events are equally likely in any probability procedure.
- This statement is NOT a principle of probability. In most situations, events are not equally likely. For example, in a deck of cards, the probability of drawing a red card is different from drawing a black card because the deck contains more black cards than red ones. In certain probability problems, events may be equally likely, but this is not a general rule that applies to all probability procedures. Events can have different probabilities depending on the specific context.
Conclusion:
While the first three statements represent fundamental principles of probability, D is incorrect because it assumes that all events are equally likely, which is not always the case in probability theory.