Probability

Summary and Exam Tips for Probability

Probability is a subtopic of Statistics, which falls under the subject Mathematics in the Edexcel Lower Secondary curriculum. Probability helps us understand how likely an event is to occur. For instance, when tossing a coin, there are two possible outcomes: heads or tails, each with a probability of $\frac{1}{2}$. Similarly, when throwing a die, there are six possible outcomes, each with a probability of $\frac{1}{6}$. The probability of an event is calculated as the number of ways it can happen divided by the total number of outcomes. For example, the probability of picking a blue marble from a bag of 5 marbles (4 blue, 1 red) is $\frac{4}{5}$.

Mutually exclusive events cannot occur simultaneously, and their combined probability is the sum of their individual probabilities. Independent events, like tossing a coin and throwing a die, use the multiplication law to find the combined probability. Theoretical probability is based on expected outcomes, while experimental probability is based on actual results from experiments. Repeated trials help stabilize the relative frequency, providing a more accurate probability estimate. Understanding the sample space of all possible outcomes is crucial in probability calculations.

Exam Tips

• Understand Basic Concepts: Make sure you grasp the difference between theoretical and experimental probability, as well as mutually exclusive and independent events.
• Practice Calculations: Regularly practice calculating probabilities using the formula $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.
• Use Sample Space: Always list the sample space to ensure you consider all possible outcomes.
• Repeat Experiments: For experimental probability, remember that more trials lead to more accurate estimates.
• Check Your Work: Double-check calculations, especially when dealing with fractions and decimals, to avoid simple errors.