# 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:
• $\scriptsize \displaystyle P\left( \text{S} \right)=1$ (where $\scriptsize \displaystyle \text{S}$ 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: $\scriptsize \displaystyle P\left( {\text{A or B}} \right)=P\left( \text{A} \right)+P\left( \text{B} \right)$
• Complementary events and is therefore able to calculate the probability of an event not occurring
• $\scriptsize \displaystyle P\left( {\text{A or B}} \right)=P\left( \text{A} \right)+P\left( B \right)-P\left( {\text{A and B}} \right)$ (where $\scriptsize \displaystyle \text{A}$and $\scriptsize \displaystyle \text{B}$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: $\scriptsize \displaystyle P\left( {\text{A and B}} \right)=P\left( \text{A} \right)\cdot P\left( \text{B} \right)$.)
• 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 $\scriptsize P~\left( {\text{A }\!\!~\!\!\text{ and }\!\!~\!\!\text{ B}} \right)~=~P~\left( \text{A} \right).P~\left( \text{B} \right)$.
• Use the addition rule for mutually exclusive events $\scriptsize P\left( {\text{A }\!\!~\!\!\text{ or }\!\!~\!\!\text{ B}} \right)=~P\left( \text{A} \right)+~P\left( \text{B} \right)$.
• Use $\scriptsize P(\text{A or B)}=P\text{(A)}+P\text{(B)}-P\text{(A and B)}$ when $\scriptsize P\left( {\text{A}\cap \text{B}} \right)\ne 0$.

### 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.