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In probability, one of the fundamental rules is that the likelihood of any event occurring must fall within a specific range. This range lies between 0 and 1, inclusive. These boundaries signify impossible and certain events, respectively.

The value of 0 means that the event cannot possibly happen, while a value of 1 indicates absolute certainty of occurrence. Any value that strays from this range does not represent a proper probability because it suggests that an event might be less than impossible or more than certain, which is logically inconsistent in probability theory.

Let's illustrate: if we consider the probability of rolling a die and getting a six as 0, it means it's impossible to roll a six, which isn't correct for a fair die. Conversely, if we say the probability of getting a six is 9.9, it suggests a greater than certain chance, which makes no practical sense. Thus, all valid probability values must conform to this 0 to 1 range.

Understanding the specific values that can be considered valid probabilities is crucial for clear mathematical reasoning. Each value, whether it be a fraction, decimal, or percentage, must first strictly adhere to the probability range.

For instance, in our exercise, 99% needs to be converted to its decimal form. This is achieved by dividing by 100, which results in 0.99. Because 0.99 falls within the range of 0 to 1, it can be considered a valid probability.

However, the value 9.9 exceeded this range as it is a number greater than 1, thus it cannot represent a probable event. Similarly, negative values are not permissible in probability since probabilities cannot be less than zero, hence, values like -0.90 will automatically be rejected as improbable by definition.

• All potential probabilities must be non-negative.
• They must not exceed the value of 1.
• Convert percentages to decimals to assess validity.

Conducting a probability analysis involves systematically reviewing potential values and determining whether they can be probabilities according to the defined criteria.

The analysis involves checking each number to see if it fits within the probability range between 0 and 1, as demonstrated in step-by-step solutions. For example, a value of 0.9 comfortably fits within our range, indicating it can indeed be a probability. On the other hand, a number like 9.9 falls outside the accepted limits and must be ruled out.

An analysis is not just about checking ranges but also ensuring logical consistency. Observe trends and provide justification for inclusion or exclusion as probabilities:

• Verify each number's position relative to the 0 to 1 range.
• Transform percentages into fractions or decimals if necessary.
• Justify why a number can or cannot be a probability.

Such thoughtful analysis is essential to correctly interpret and apply probabilities in both theoretical and real-world scenarios.