Edexcel International A Level
Statistics 1 (YMA01)
Basic Probability
Comprehensive revision guide with diagrams for probabilities, events, Venn diagrams, and tree diagrams
What Language is Used in Probability?
Experiment: A repeatable activity that has a result that can be observed or recorded. It is what is happening in a question.
Outcome: The result of an experiment.
Sample Space: All possible outcomes can be shown in a sample space – this may be a list or a table and is particularly useful when it is difficult to envisage all possible outcomes in your head.
Event: An outcome or a collection of outcomes; it is what we are interested in happening. An event could be more than one outcome.
Sample Space Example
📊 Sample Space: Product of Two Fair Four-Sided Spinners
Terminology: 'and', 'or', 'not'
✓ Key Terminology:
- A and B: Both events A and B happen at the same time (written as A ∩ B)
- A or B: Event A happens, or event B happens, or both happen (written as A ∪ B)
- Not A: Event A does not happen (written as A')
Notation and Basic Probability
P(A) = 0.6 → "the probability of event A happening is 0.6"
P(A') = 0.4 → "the probability of event A not happening is 0.4"
P(not A) = 1 − P(A)
✓ Basic Probability Formula:
P("success") = Number of ways to get "success" / Total number of outcomes
This formula only applies if all outcomes are equally likely.
⚠ Important Distinction:
- Theoretical Probability: Based on what should happen (e.g., rolling a fair die)
- Relative Frequency: Based on experimental results (e.g., outcomes from actually rolling a die many times)
- Compare the two to detect bias in an experiment
What are Independent Events?
Independent Events: Events that do not affect each other. The probability of one event happening is unaffected by the outcome of the other event.
✓ Independent Events Rule:
P(A AND B) = P(A) × P(B)
Example: Rolling a 6 on a dice AND flipping heads on a coin = 1/6 × 1/2 = 1/12
What are Mutually Exclusive Events?
Mutually Exclusive Events: Events that cannot occur simultaneously. The outcome of one event means the other event cannot occur.
✓ Mutually Exclusive Events Rule:
P(A OR B) = P(A) + P(B)
Example: Rolling a 5 on a die OR rolling a 6 = 1/6 + 1/6 = 2/6 = 1/3
Comparison: Independent vs Mutually Exclusive
| Aspect |
Independent Events |
Mutually Exclusive Events |
| Definition |
Do not affect each other |
Cannot happen at the same time |
| AND/OR |
AND is used (×) |
OR is used (+) |
| Formula |
P(A AND B) = P(A) × P(B) |
P(A OR B) = P(A) + P(B) |
| Example |
Rolling a die twice |
Rolling a 5 or 6 on one die |
| P(A AND B) |
Can be non-zero |
Always equals 0 |
| Relationship |
Can be independent AND mutually exclusive |
Cannot be independent |