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When we talk about "outcomes" in probability, we're referring to all the possible results that can occur from a given experiment. In the case of tossing a penny three times, each individual toss has two possible results: either heads or tails. This is a classic example in probability, as it's a simple way to understand how outcomes work. For three coin tosses:

• First toss has two outcomes: heads (H) or tails (T).
• Second toss also has two outcomes: H or T.
• Third toss again has two outcomes: H or T.

To determine the total number of outcomes from all three tosses, we multiply the outcomes of each toss: \[2 \times 2 \times 2 = 2^3 = 8\]. Thus, there are 8 possible outcomes for the three coin tosses.

In probability, an "event" refers to a specific outcome or a set of outcomes of an experiment. It's essentially what you are interested in finding the probability for. For the exercise at hand, we want to determine the probability of the event where exactly 2 heads and 1 tail are observed after 3 coin tosses. Let's identify these outcomes:

• HHT (Heads, Heads, Tails)
• HTH (Heads, Tails, Heads)
• THH (Tails, Heads, Heads)

These are the only possible outcomes where we achieve the desired event of 2 heads and 1 tail. Since there are 3 such outcomes, they collectively define our event of interest.

To find the probability of any event, we use the concept of a "ratio". This is essential because probability is essentially a comparison between the number of favorable outcomes and the total number of possible outcomes. In mathematical terms, probability is expressed as:\[\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}\]In our exercise, we have 3 favorable outcomes (HHT, HTH, and THH) for our event of getting 2 heads and 1 tail. Meanwhile, there are a total of 8 outcomes when the coin is tossed three times. Using the ratio, the probability becomes:\[\frac{3}{8}\]This ratio tells us how likely the event is to happen. Since the ratio is less than 1, it indicates that getting 2 heads and 1 tail in 3 coin tosses isn't a certainty, but it's certainly possible.