Probability

Summary and Exam Tips for Probability

Probability is a subtopic of Statistics and Probability, which falls under the subject Mathematics in the Cambridge Lower Secondary curriculum. Probability helps us understand how likely events are to occur. For instance, when tossing a coin, there are two possible outcomes: heads (H) or tails (T), each with a probability of $\frac{1}{2}$. Similarly, when throwing a single die, there are six possible outcomes (1 through 6), each with a probability of $\frac{1}{6}$.

The probability of an event happening is calculated as the number of ways it can happen divided by the total number of outcomes. For example, the probability of rolling a "4" on a die is $\frac{1}{6}$, and picking a blue marble from a bag of 5 marbles (4 blue, 1 red) is $\frac{4}{5}$.

In cases of unfair dice or spinners with unequal sectors, the relative frequency approach is used, where the experiment is repeated until the relative frequency stabilizes. 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. For more accurate estimates, experiments should be repeated multiple times. The sample space includes all possible outcomes, such as the 52 cards in a deck.

Exam Tips

• Understand Key Concepts: Make sure you grasp the difference between theoretical and experimental probability, as well as how to calculate probabilities for simple events like coin tosses and dice rolls.
• Practice Problems: Work through examples involving mutually exclusive and independent events to solidify your understanding.
• Use Relative Frequency: For experiments with unequal outcomes, remember to use relative frequency and repeat trials to get a stable estimate.
• Sample Space: Always consider the sample space to ensure you account for all possible outcomes in probability calculations.
• Review and Repeat: The more you practice, the better you'll understand the concepts, so repeat experiments and calculations to improve accuracy.