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When we talk about the outcomes of a coin toss in probability, we are referring to the different results that can occur from this activity. A standard coin has two sides—often referred to as 'Heads' (H) and 'Tails' (T). This is a classic example of a simple experiment in probability because it has a small and easy to understand sample space. The sample space is a term used in probability to describe the set of all possible outcomes that can occur.

For a single coin toss, the sample space is concise:

• Heads (H)
• Tails (T)

Since there are no other sides to a coin, these are the only two outcomes we consider when discussing the probability of a coin toss.

Moving on from the coin toss, let's consider another commonly analyzed activity in probability: throwing a die. A standard die is a six-sided cube with each of its six faces showing a different number of dots from 1 to 6. Each throw of the die can result in one of these six numbers, providing us with a clear sample space for this experiment.

The outcomes are simply the numbers on the die:

• 1
• 2
• 3
• 4
• 5
• 6

Throwing a die is a bit more complex than tossing a coin due to the increased number of outcomes. However, it still represents a finite and very manageable sample space that is fundamental to understanding basic probability concepts.

Combining probabilities is a vital concept when dealing with more complex experiments that involve more than one activity, like tossing a coin and throwing a die simultaneously. To calculate the sample space for a combined experiment, you multiply the number of outcomes from each individual activity.

In our example, combining a coin toss and a die throw multiplies the 2 possible outcomes of the coin (Heads or Tails) with the 6 possible outcomes of the die (1 through 6), resulting in a total of 12 unique outcomes. This can be visualized as creating pairs from each outcome of the first event with every outcome of the second event.

Visualizing Combined Outcomes

The resulting sample space for the combined experiment looks like this:

• (H,1)
• (H,2)
• ... and so on until (T,6)

Understanding this method of combining outcomes allows students to tackle more complex probability questions where several events are considered at once.