Data Handling - Chance and Probability

Chance and Probability: Chance is the possibility of an event occurring in a random situation, while Probability is the numerical representation of that chance. For example, saying it 'might' rain is a statement of chance. Visualize a weather forecast where 'might' is replaced by a percentage like 70%.

Random Experiment: An experiment where the outcome cannot be predicted with 100% certainty. Common examples include tossing a coin or spinning a wheel. Imagine a spinner with different colored sections; you know it will land on a color, but you don't know which one until it stops.

Outcomes and Sample Space: An outcome is a possible result of an experiment. The collection of all possible outcomes is called the sample space. Visualizing a 'Tree Diagram' is helpful here; imagine a starting point that splits into branches for every possible result, such as one branch for 'Heads' and one for 'Tails' when tossing a coin.

Equally Likely Outcomes: Outcomes are equally likely if each has the same chance of occurring. A fair six-sided die is a perfect visual example; since every face is the same size and the die is not weighted, landing on a $1$ is just as likely as landing on a $6$.

Event: An event is a specific outcome or a set of outcomes from an experiment. For instance, in rolling a die, 'getting an even number' is an event that includes the outcomes $2, 4,$ and $6$. Imagine circling specific numbers on a list of all possible outcomes to define your event.

Probability Scale: Probability values always range from $0$ to $1$. Visualize a horizontal number line: $0$ at the far left represents an 'Impossible Event' (like rolling a $7$ on a standard die), $1$ at the far right represents a 'Certain Event' (like the sun rising), and $\frac{1}{2}$ in the center represents an 'Even Chance' (like a coin flip).

Complementary Events: These are events that represent the 'not' case of an outcome. If the probability of an event happening is $P(E)$, the probability of it not happening is $1 - P(E)$. Visualise a pie chart where one slice is the event and the rest of the pie is the complement; together they make a whole circle ($1$).