Probability - advanced

This lesson comprises three (3) master classes focusing on:

• Probability language
• Venn diagrams, tree diagrams and two-way tables
• Combining probabilities of events
• Multi-stage chance experiments
• Models and simulations of probability experiments

Content:

MA5-PRO-C-01

Describe multistage chance experiments involving independent and dependent events

• Explain the difference between dependent and independent events in experiments involving 2 stages
• Explain how the probability of independent and dependent events differs in relation to replacement

Solve problems for multistage chance experiments

• Record all possible outcomes for multistage chance experiments
• Determine the probabilities of outcomes for multistage independent events using \( P(A\ and\ B)=P(A) \times P(B) \), where necessary
• Determine the probabilities of outcomes for multistage dependent events
• Associate complementary events with probabilities in multistage chance experiments

Design and use simulations to model and examine situations involving probability

• Design and conduct a probability simulation, modelling probabilities of events, using digital tools
• Record and use the results of a probability simulation to predict future events
• Apply reasoning to evaluate the simulation and its related outcomes

MA5-PRO-P-01

Solve problems involving Venn diagrams and 2-way tables

• Represent and interpret data in Venn diagrams for mutually exclusive and non-mutually exclusive events
• Construct Venn diagrams to represent all possible combinations of 2 attributes from given or collected data
• Interpret data in 2-way tables to represent relationships between attributes
• Construct 2-way tables to represent the relationships between attributes
• Convert between representations of the relationships between 2 attributes in Venn diagrams and 2-way tables
• Define a set as a collection of distinct objects
• Use Venn diagrams, set language and notation for events, including \( \bar{A} \)  (or \( A' \) or \( A^c \)) for the complement of an event \( A \), \( A \cap B \) for ' A and B' (the intersection of events A and B) and \( A \cup B \) for 'A or B' (the union of events A and B) and recognise mutually exclusive events

Use the language, 'if … then', 'given', 'of' and 'knowing that', to examine conditional statements and identify common mistakes in interpreting the language

• Calculate the probabilities of events where a condition restricts the sample space
• Describe the effect of a given condition on the sample space
• Identify conditional statements used in descriptions of chance situations
• Explain the validity of conditional statements when describing chance situations, referring to dependent and independent events
• Identify and explain common misconceptions relating to chance experiments

Describe mutually and non-mutually exclusive events using specific language and calculate related probabilities

• Explain the difference between mutually exclusive and non-mutually exclusive events
• Describe compound events using the terms inclusive or and exclusive or
• Describe non-mutually exclusive events using the terminology and, inclusive or and exclusive or
• Describe events using the terms at least, at most, not and and
• Calculate the probability of compound events using strategies including Venn diagrams and 2-way tables