Data Handling - Introduction to Probability

A Random Experiment is a process where the result cannot be predicted with certainty. For example, tossing a coin is an experiment where you can see two possible outcomes: Heads or Tails. Visually, this is represented by the two distinct sides of the coin.

The Sample Space is the set of all possible outcomes of an experiment, denoted by $S$. Visually, if you roll a six-sided die, the sample space is $S = \{1, 2, 3, 4, 5, 6\}$, which can be visualized as the six numbered faces of a cube.

An Event is a specific outcome or a subset of the sample space. For instance, when rolling a die, 'getting an even number' is an event $E = \{2, 4, 6\}$. You can visualize this as selecting specific elements from the total set of outcomes.

Equally Likely Outcomes occur when each result in the sample space has the same chance of happening. For a fair die, each face from $1$ to $6$ is physically identical in size and weight, ensuring no face is favored over another.

Probability is a numerical value that ranges from $0$ to $1$, describing how likely an event is to occur. On a visual probability scale (a horizontal number line), $0$ indicates an 'Impossible Event' at the far left, $1$ indicates a 'Sure Event' at the far right, and $0.5$ represents an 'Even Chance' in the exact center.

Complementary Events are two outcomes that are the only possibilities and whose probabilities sum to $1$. If $E$ is the event of 'it raining', then 'it not raining' is the complement, denoted as $\overline{E}$. Together, they cover the entire visual area of the sample space.

An Impossible Event has a probability of $0$ because it can never happen, such as drawing a blue marble from a bag containing only red marbles. A Sure Event has a probability of $1$ because it is certain to happen, like rolling a number less than $7$ on a standard die.