# Data handling: Use experiments, simulation and probability distribution to set and explore probability models

### Subject outcome

Subject outcome 4.3: Use experiments, simulation and probability distribution to set and explore probability models

### Learning outcomes

- Explain and distinguish between the following terminology/events:
- Probability
- Dependent events
- Independent events
- Mutually exclusive
- Mutually inclusive
- Complementary events.

- Make predictions based on validated experimental or theoretical probabilities taking the following into account:
- [latex]\scriptsize \displaystyle P\left( \text{S} \right)=1[/latex] (where [latex]\scriptsize \displaystyle \text{S}[/latex] is the sample space)
- Disjoint (mutually exclusive) events, and is therefore able to calculate the probability of either of the events occurring by applying the addition rule for disjoint events: [latex]\scriptsize \displaystyle P\left( {\text{A or B}} \right)=P\left( \text{A} \right)+P\left( \text{B} \right)[/latex]
- Complementary events and is therefore able to calculate the probability of an event not occurring
- [latex]\scriptsize \displaystyle P\left( {\text{A or B}} \right)=P\left( \text{A} \right)+P\left( B \right)-P\left( {\text{A and B}} \right)[/latex] (where [latex]\scriptsize \displaystyle \text{A}[/latex]and [latex]\scriptsize \displaystyle \text{B}[/latex]are events within a sample space)
- Correctly identify dependent and independent events

(e.g. from two-way contingency tables or Venn diagrams) and therefore appreciate when it is appropriate to calculate the probability of two independent events occurring by applying the product rule for independent events: [latex]\scriptsize \displaystyle P\left( {\text{A and B}} \right)=P\left( \text{A} \right)\cdot P\left( \text{B} \right)[/latex].)

- Draw tree diagrams, Venn diagrams and complete contingency two-way tables to solve probability problems (where events are not necessarily independent).

Range:- Venn diagrams to be limited to two subsets.
- Tree diagrams where the sample space is manageable (not more than 15 possible outcomes).

- Interpret and clearly communicate results of the experiments correctly in terms of real context.

### Unit 1 outcomes

By the end of this unit you will be able to:

- Understand the difference between independent and dependent events.
- Understand the difference between mutually inclusive and mutually exclusive events.
- Understand complementary events.
- Identify independent and dependent events using [latex]\scriptsize P~\left( {\text{A }\!\!~\!\!\text{ and }\!\!~\!\!\text{ B}} \right)~=~P~\left( \text{A} \right).P~\left( \text{B} \right)[/latex].
- Use the addition rule for mutually exclusive events [latex]\scriptsize P\left( {\text{A }\!\!~\!\!\text{ or }\!\!~\!\!\text{ B}} \right)=~P\left( \text{A} \right)+~P\left( \text{B} \right)[/latex].
- Use [latex]\scriptsize P(\text{A or B)}=P\text{(A)}+P\text{(B)}-P\text{(A and B)}[/latex] when [latex]\scriptsize P\left( {\text{A}\cap \text{B}} \right)\ne 0[/latex].

### Unit 2 outcomes

By the end of this unit you will be able to:

- Understand when to use Venn diagrams.
- Draw Venn diagrams.
- Interpret Venn diagrams.

### Unit 3 outcomes

By the end of this unit you will be able to:

- Draw tree diagrams when appropriate.
- Use tree diagrams to solve probability problems.

### Unit 4 outcomes

By the end of this unit you will be able to:

- Draw and complete contingency tables.
- Use contingency tables to solve probability problems.