Probability of Combined Events
Use sample space diagrams and the idea of independent events to find the probability of two events.
Overview
Building on single-event probability, Year 9 students find the probability of two events happening together. They list outcomes in sample space diagrams, recognise independent events, and use the multiplication idea for combined probabilities. This leads directly into the tree diagrams and combined probability of IGCSE.
What You Will Learn
- List all outcomes of two events using a sample space diagram
- Find the probability of a combined event from a sample space
- Understand what makes two events independent
- Multiply probabilities to find the chance of two independent events both happening
- Use the fact that probabilities of all outcomes add up to 1
Key Vocabulary
Common Mistakes to Avoid
- Missing outcomes when listing a sample space
- Adding probabilities when you should multiply for 'and'
- Assuming events are independent when one affects the other
- Not simplifying the final probability fraction
What Comes Next
At IGCSE this develops into tree diagrams, conditional probability and 'without replacement' problems in the Probability topic.
Frequently Asked Questions
What is a sample space diagram?
It is a table or list showing every possible outcome of two events. For two dice, it lists all 36 combinations, which makes it easy to count the outcomes you want and find a probability.
When do I multiply probabilities?
Multiply when you want two independent events to both happen ('this AND that'). For example, the probability of two heads when flipping a coin twice is ½ × ½ = ¼.
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Statistics and Probability
- Framework ref
- 9Sp
- Difficulty
- Medium
Build strong foundations in Probability of Combined Events
A free trial class with Teacher Rig helps your Year 9 child master Probability of Combined Events now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Probability of Combined Events develops in IGCSE Probability (Cambridge 0580) →