Which of the following is NOT a principle of probability?
A) The probability of any event is between 0 and 1 inclusive.
B) All events are equally likely in any probability procedure.
C) The probability of an event that is certain to occur is 1.
D) The probability of an impossible event is 0.
The Correct Answer and Explanation is :
The correct answer is B) All events are equally likely in any probability procedure.
Explanation:
The principles of probability are fundamental rules that help quantify uncertainty and the likelihood of events occurring. Let’s break down each option:
A) The probability of any event is between 0 and 1 inclusive.
- This is a core principle of probability. The probability of any event ( P(E) ) is always a number between 0 and 1, where:
- ( P(E) = 0 ) means the event will not occur (an impossible event),
- ( P(E) = 1 ) means the event will definitely occur (a certain event).
- Any value in between represents events that are likely to occur to varying degrees. Therefore, this is a true statement and a valid principle of probability.
B) All events are equally likely in any probability procedure.
- This is NOT a general principle of probability. While some probability problems assume all events are equally likely (this is called the uniform probability model), it is not a rule for all probability situations. In most real-world scenarios, events may have different probabilities of occurring. For instance, when rolling a biased die, some outcomes are more likely than others. So, events are not always equally likely, making this option incorrect.
C) The probability of an event that is certain to occur is 1.
- This is another valid principle. If an event is certain to happen (like the sun rising tomorrow), its probability is 1. This reflects the idea that a probability of 1 represents certainty.
D) The probability of an impossible event is 0.
- This is also true. An event that cannot happen, such as drawing a card from a deck that doesn’t exist, has a probability of 0. It signifies impossibility.
In summary, while the other statements are correct principles of probability, statement B is false because not all events are guaranteed to be equally likely in every probability context.