Data Handling - Probability: Basic concepts and simple problems

A Random Experiment is an action where the result cannot be predicted with total certainty before it happens, such as tossing a coin or rolling a die. Visualise a coin spinning in the air; until it lands and stops, you do not know if it will show Heads or Tails.

An Outcome is a possible result of a single trial of an experiment. For example, if you roll a six-sided die, the possible outcomes are $1, 2, 3, 4, 5,$ or $6$. Imagine the die face-up on a table showing a specific number of dots.

The Sample Space is the set of all possible outcomes of an experiment, usually denoted by $S$. For a coin toss, the sample space is $S = \{H, T\}$. Visualise this as a boundary or a box that contains every single result that could possibly happen.

An Event is a specific outcome or a collection of outcomes that we are interested in, which is a subset of the sample space. For instance, in rolling a die, 'getting an even number' is an event containing the outcomes $\{2, 4, 6\}$.

Equally Likely Outcomes occur when every outcome in the sample space has the same chance of happening. Imagine a fair spinner divided into four equal quarters of different colors; because the area for each color is the same, the needle is equally likely to land on any color.

The Probability of an Event, denoted as $P(E)$, is a numerical measure of the likelihood that the event will occur. It is always a value between $0$ and $1$ inclusive. Imagine a 'Probability Scale' line where $0$ represents an 'Impossible Event' (like drawing a blue card from a deck of only red cards) and $1$ represents a 'Certain Event' (like the sun rising).

An Impossible Event has a probability of $0$. For example, the probability of rolling a $7$ on a standard six-sided die is $0$ because the faces are only numbered $1$ through $6$.

A Sure or Certain Event has a probability of $1$. For example, if a bag contains only red balls, the probability of drawing a red ball is $1$ because there is no other possibility.