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A sample space is a fundamental concept in probability. It refers to the set of all possible outcomes of a particular experiment. In our traffic light problem, the sample space includes all possible sequences of red (R) and green (G) lights that you can encounter on a journey. With three lights to pass and each light having two color possibilities, we calculate the sample space by raising the number of possibilities for one light to the power of the number of lights, i.e., \(2^3\), resulting in 8 outcomes.
Thus, the sample space here is

• RRR
• RRG
• RGR
• GRR
• RGG
• GRG
• GGR
• GGG

Listing the sample space helps us in determining probabilities for specific events, like encountering red lights.

In probability, an outcome refers to a possible result of an experiment, which in this case is each sequence of light colors you drive through. Each sequence is a unique outcome, such as 'RRG' or 'GGG'.
Since all outcomes in our scenario have an equal likelihood of occurring, each individual outcome has a probability of \(\frac{1}{8}\), as there are 8 possible sequences. Recognizing each outcome distinctively is essential for future probability calculations, especially when specifying exact conditions to analyze, such as having only one red light.

Once the sample space is determined, calculating the probability of specific events becomes straightforward. Probability is calculated as the number of desired outcomes divided by the total number of possible outcomes.
To find the probability of stopping at exactly one red light during your trip (for example, outcomes RGG, GRG, and GGR), count these specific outcomes and divide by the total. Here, there are 3 such outcomes from the 8 possibilities, yielding a probability of \(\frac{3}{8}\). On the other hand, calculating the probability of encountering at least one red light involves subtracting the probability of an event's complement from 1. Since only 'GGG' has no red lights, at least one red light's probability is \(1 - \frac{1}{8} = \frac{7}{8}\).

The traffic light problem is an excellent example to practice understanding probability concepts like sample space, outcomes, and probability calculations. Here, the problem addresses a real-world situation where you encounter traffic lights on your way somewhere.
This exercise practices these concepts by introducing variability with red and green lights and exploring possibilities through probability.
Such problems are valuable as they help comprehend how probability works in everyday scenarios and teach essential analytical skills for evaluating events, outcomes, and their likelihood.