Making and Justifying Decisions Based on Probability

Familiarise with the concept of probability as the measure of the likelihood of an event happening.
Recognise that probabilities always lie between 0 (the event never happens) and 1 (the event is certain).
Understand that the sum of all probabilities for all possible outcomes in an event is 1.
Know that if a probability is close to 0, it is very unlikely to occur, and if it is close to 1, it is very likely to occur.

Know how to identify theoretical probability, which is determined through mathematical reasoning. For example, the theoretical probability of rolling an even number with a six-sided die is 0.5, because there are three even numbers (2, 4, 6) out of a total of six possible outcomes.
Understand experimental probability, which is based on actual experiments and observations. For example, if you rolled a die 100 times and rolled an even number 57 times, the experimental probability of rolling an even number would be 0.57.

Recognise how you can use probability to support decision-making processes. For instance, you might decide whether to participate in a game based on your chances of winning or losing.
Understand that when comparing probabilities, the option with the higher probability might be the better choice, if the aim is to maximise the chance of a particular outcome.
Be aware that actual outcomes can differ from expected probabilities, with the law of large numbers stating that actual outcomes tend to align with expected probabilities more closely as more trials are performed.

Be able to apply probability in various real-life contexts such as in forecasting weather, insurance risks, game strategies, or medical treatments.
Know how to translate these real-life situations into a probability problem. For instance, recognising the total possible outcomes, and the specific outcomes of interest.

Understand that it is essential to justify the decisions made based on probability, taking into account not just the numerical probability, but also the context and potential consequences of different outcomes.
Know how to articulate your decision-making reasoning in clear terms, referencing relevant probabilities and the measurement of risk vs. reward.
Be aware that often decisions made based on probability involve balancing potential gains against possible risks, justifying that balance is key to a good decision-making.
Recognise that your justifications may vary depending on the audience. For internal reflections, focus on improving your understanding and judgment. For external justifications, aim to be clear, concise, and convincing to others.