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When evaluating probability problems, it's essential to understand the idea of mutually exclusive events. In simple terms, mutually exclusive events are events that cannot happen at the same time. For instance, the problem states that a worker either drives a car or takes public transportation to work. These two scenarios cannot occur simultaneously, making them mutually exclusive. This is mathematically represented as:  \[P(A \text{ and } B) = 0\] Since driving and public transportation are mutually exclusive events, we can simplify the union formula:  \[P(A \text{or} B) = P(A) + P(B)\] Mutual exclusivity here helps us directly add the individual probabilities of driving a car and taking public transportation without needing any overlap consideration.

Another critical principle in probability is the complement rule. This rule is useful when we want to find the probability of an event not happening. The complement of an event A is denoted as A^c and represents all outcomes where event A does not occur. The formula for the complement is:  \[P(A^c) = 1 - P(A)\] In our exercise, part (b) requires calculating the probability that a worker neither drives nor takes public transportation. This can be found by taking the complement of the event that a worker either drives or takes public transportation:  \[P(A^c \text{ and } B^c) = 1 - P(A \text{ or } B)\] Similarly, part (c) asks for the probability that a worker does not drive to work. We use the complement rule again:  \[P(A^c) = 1 - 0.867 = 0.133\] The complement rule simplifies calculations by focusing on the event's absence rather than its presence.

The concept of the union of events is essential for combining probabilities. The union of two events A and B, denoted as A ∪ B, represents all outcomes that are in A, B, or both. To calculate the union of non-mutually exclusive events, we use the formula:  \[P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\] However, if the events are mutually exclusive (as in our exercise), where no outcomes are common, the formula simplifies to:  \[P(A \text{ or } B) = P(A) + P(B)\] In our exercise, we use this idea to find the probability that a worker either drives a car or takes public transportation:  \[0.867 + 0.048 = 0.915\] Thus, the union of mutually exclusive events helps us combine their probabilities straightforwardly.