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Combinations in probability help us understand how different outcomes come together. In the context of our coin toss experiment, each toss of the coin can result in either heads (H) or tails (T).
When a coin is tossed twice, we pair each result of the first toss with each result of the second toss.
This generates all possible combinations of outcomes:

• HH (Heads on both tosses)
• HT (Heads on first, Tails on second)
• TH (Tails on first, Heads on second)
• TT (Tails on both tosses)

This understanding of combinations is fundamental to more complex probability problems.
By breaking the problem into parts and combining their results, we can figure out all possible outcomes in a given scenario.

Each experiment in probability has several possible outcomes. In our coin toss example, an 'outcome' refers to the result of one or more coin tosses.
When we toss a coin twice, there are four possible outcomes:

• HH
• HT
• TH
• TT

These outcomes are comprehensive, reflecting all potential results of the two-toss experiment.
Listing all possible outcomes is vital because it defines the 'sample space' of the experiment.
It ensures that we have considered every scenario that can occur.
Understanding the possible outcomes makes it easier to calculate probabilities.

Probability theory is the branch of mathematics that deals with uncertainty. It helps us calculate the likelihood of different outcomes.
In our coin toss example, probability theory tells us that each toss of the coin is an independent event, with two possible outcomes: heads (H) or tails (T).
The probability of each outcome in a fair coin toss is 0.5.
When we toss the coin twice, we use combinations to list all possible outcomes (HH, HT, TH, TT).
The probability of each of these combined outcomes is found by multiplying the probabilities of the individual events.
Thus, the probability of getting HH, HT, TH, or TT is ewline 0.5 * 0.5 = 0.25.
Probability theory not only helps us list outcomes but also shows how likely each outcome is. This is crucial for making predictions and informed decisions based on data.