Which of the following is not a principle of probability?

• A. The probability of an event can be greater than $1$ if the event is certain.
• B. The sum of probabilities of all possible outcomes in a sample space is $1$.
• C. The probability of any event is always between $0$ and $1$, inclusive.
• D. The probability of the union of two mutually exclusive events is the sum of their individual probabilities.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the basic principles of probability. These include: (a) The probability of any event is between 0 and 1, inclusive; (b) The sum of probabilities of all possible outcomes in a sample space is 1; (c) For mutually exclusive events, the probability of their union is the sum of their individual probabilities.
2. Step 2: Analyze the statement 'The probability of an event can be greater than 1 if the event is certain.' Recall that a certain event has a probability of exactly 1, and probabilities cannot exceed 1 by definition.
3. Step 3: Compare each given statement against the fundamental principles of probability to identify which one contradicts these principles.
4. Step 4: Recognize that the statement claiming a probability greater than 1 is not valid because probabilities are always between 0 and 1, inclusive.
5. Step 5: Conclude that the incorrect principle is the one stating that the probability of an event can be greater than 1 if the event is certain, as this violates the fundamental rules of probability.