Data Handling - Probability and Likelihood

Probability is the measure of how likely an event is to occur, ranging from $0$ to $1$. It helps us predict the chance of something happening, even if we are not certain of the result.

The Probability Scale is a visual tool represented as a straight horizontal line. On the far left, we mark 'Impossible' ($0$). In the exact center, we mark 'Even Chance' ($\frac{1}{2}$ or $50\%$), and on the far right, we mark 'Certain' ($1$). Outcomes fall somewhere along this line based on their likelihood.

Likelihood Words are used to describe the chances of an event. 'Impossible' means it can never happen; 'Unlikely' means it has a small chance; 'Even Chance' means it is just as likely to happen as not; 'Likely' means it has a good chance; and 'Certain' means it will definitely happen.

Outcomes and Sample Space refer to all the possible results of an experiment. For example, if you roll a standard $6$-sided die, the sample space consists of the visual dots representing numbers $\{1, 2, 3, 4, 5, 6\}$. Each number is a possible outcome.

Fairness in games means every possible outcome has an equal chance of occurring. A fair spinner is visually represented as a circle divided into equal-sized 'slices' or sectors. If one color occupies a larger area than others, the spinner is 'biased' or unfair.

Frequency and Data Recording involves tracking how often an event occurs during a trial. This is often displayed in a tally chart where four vertical lines and one diagonal strike represent a group of $5$, making it easy to see which outcome happened most often.

Theoretical Probability is what we expect to happen based on math, while Experimental Probability is what actually happens when we repeat an experiment. For instance, if you flip a coin $10$ times, you expect $5$ heads (theoretical), but you might actually get $6$ (experimental).