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In probability, mutually exclusive events are events that cannot happen at the same time. If one event occurs, the other cannot. Consider the events A and B defined in the original exercise. Event A is picking a blue card then landing a head in the coin toss. Event B is picking a red or green card, also landing a head. Looking at these events, they are mutually exclusive because if you pick a blue card (for event A), you cannot simultaneously pick a red or green card (for event B).

This is crucial because it impacts how we calculate the probabilities of combined events. For mutually exclusive events, the probability of either event A or event B occurring is simply the sum of their probabilities. In symbol form, this means:

• If events A and B are mutually exclusive, then: \( P(A \cup B) = P(A) + P(B) \)

By understanding them better, especially in experiments like coin tosses coupled with card selections, one grasps the essence of probability setups and decision-making in real-life scenarios.

The sample space is an essential concept in probability, representing all possible outcomes of an experiment. It is like a comprehensive list of every possible result that can happen when the experiment is performed.

For the special deck of cards with associated coin tosses, the sample space consists of all combinations of card colors (green, blue, red) and coin toss outcomes (head or tail). This results in different pairs; for instance, picking a green card and tossing a head (G, H) or a blue card and tossing a tail (B, T). In this exercise, because there are ten cards and each card instance is followed by a coin toss with two possible outcomes, the total sample space contains 20 outcomes.

Understanding the sample space is important so that you can determine the probability of single events or combinations of events. By identifying all the potential outcomes, you ensure you fully account for what's possible, making probabilistic calculations more accurate and reliable.

Experimental probability involves finding the likelihood of an event occurring based on the actual results of an experiment. It's different from theoretical probability, which is based solely on an understanding of events and outcomes.

When dealing with card picking and coin tossing, experimental probability allows observing actual results to calculate probabilities. For example, if after multiple trials of picking cards and tossing a coin, you observed that a blue card followed by heads occurred 3 out of 20 times, then the experimental probability for this event would be \( P(A) = \frac{3}{20} \).

This type of probability provides a real-world check against expected outcomes and can be particularly useful for making predictions based on observed data. It's important to conduct enough trials to get reliable data, which will lead to probabilities that reflect reality more closely.