Data Handling - Calculating Simple Probabilities

Probability is a measure of how likely an event is to happen, represented by a value between $0$ and $1$ inclusive. It can be expressed as a fraction, a decimal, or a percentage.

The Probability Scale is a visual tool used to describe the likelihood of events. Imagine a horizontal number line starting at $0$ (Impossible) and ending at $1$ (Certain). The midpoint $0.5$ or $\frac{1}{2}$ represents an 'Even Chance' (like a coin flip). Outcomes between $0$ and $0.5$ are 'Unlikely,' while outcomes between $0.5$ and $1$ are 'Likely.'

The Sample Space is the set of all possible outcomes of an experiment. For example, if you visualize a standard spinner divided into four equal sections colored Red, Blue, Green, and Yellow, the sample space is $\{Red, Blue, Green, Yellow\}$.

An Event is a specific outcome or a collection of outcomes from the sample space that we are interested in. For instance, if rolling a six-sided die, the event 'rolling an even number' includes the outcomes $\{2, 4, 6\}$.

Equally Likely Outcomes occur when every possible result in an experiment has the same chance of happening. For example, on a fair six-sided die, each face (1, 2, 3, 4, 5, and 6) has an equal probability of $\frac{1}{6}$.

Theoretical Probability is calculated based on reasoning about the possible outcomes. If you have a bag of $10$ marbles and $3$ are blue, you can logically determine the chance of picking a blue marble without actually performing the experiment.

Complementary Events represent the probability of an event NOT occurring. If the probability of it raining is $P(A)$, then the probability of it not raining is $P(\text{not } A)$, and the sum of these two probabilities always equals $1$.