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When thinking about probability, one essential concept is understanding *mutually exclusive events*. These are events that cannot occur at the same time. A classic example is flipping a coin; the outcome can either be heads or tails, but not both simultaneously.

If two events are mutually exclusive, their probabilities add up to 1. This is because either one event occurs, or the other does. In the case of the seat belt example from the exercise, wearing a seat belt and not wearing one are mutually exclusive events. The total probability must equal 1 since one of these events must occur.

So, when given probabilities like 0.75 and 0.30 in the statement (a), we know there's an error because their sum is 1.05, which exceeds 1. This discrepancy indicates that the probabilities do not reflect mutually exclusive events correctly.

Probabilities have specific rules they must follow to make sense. Primarily, probabilities must fall between 0 and 1, inclusive. This rule is fundamental as it signifies the likelihood of an event happening, with 0 being impossible and 1 being certain.

Unfortunately, in the exercise, the claim that a red car has a probability of 1.20 breaks this cardinal rule. A probability greater than 1 is illogical in any context of probability, since it would imply something could happen more than certainly, which isn't possible. Thus, the mistake is evident in statement (b).

This serves as a reminder that when you encounter probabilities in the wild, always check that they stay within this range. It's the simplest but one of the most critical rules you'll apply time and again in probability.

Subset probability involves understanding the relationship between two related events, where one is a subset of the other. In probability terms, an event that is a subset should have a probability that is equal to or less than the probability of the event it's part of.

Take the situation in statement (c): a red car and a red sports car. A red sports car is a more specific category and thus a subset of the broader category of red cars. Hence, the probability of picking a red sports car should be less than or equal to picking any red car.

The error in announcing that the probability of a random car being a red sports car is higher than just being a red car shows a misunderstanding of subset probability. Probabilities have to align logically with the hierarchy of categories, ensuring broader categories cover the possibilities of the more specific ones. So, always ensure those numerical relationships are logically consistent.