6. Further Probability

6.01 Venn diagrams

6.02 Review of probability fundamentals

INVESTIGATION: Simulations

6.03 Theoretical probability

6.04 Conditional probability

6.05 Independent events and data

VCE 11 Methods 2023

6.03 Theoretical probability

Interactive practice questions

A standard six-sided die is rolled and then a coin is tossed.

a

Create a probability tree for this situation.

b

What is the probability of an even number and a head?

c

What is the probability of an even number, a head, or both?

Easy

3min

A standard six-sided die is rolled $358$ times.

Easy

< 1min

A person runs a marathon, and then falls ill from exhaustion. Are the events independent or dependent?

Easy

< 1min

A fair coin is tossed $600$ times.

Easy

< 1min

Outcomes

U1.AoS4.6

the properties that probabilities for a given sample space are non-negative and the sum of these probabilities is one

U1.AoS4.3

addition and multiplication principles for counting

U1.AoS4.9

apply counting techniques to solve probability problems and calculate probabilities for compound events, by hand in simple cases

U2.AoS4.1

probability of elementary and compound events and their representation as lists, grids, Venn diagrams, tables and tree diagrams

U2.AoS4.2

the addition rule for probabilities

U2.AoS4.9

solve probability problems involving tree diagrams, by hand in simple cases

U2.AoS4.8

calculate probabilities for compound events using rules and tree diagrams, by hand in simple cases

U2.AoS4.4

the law of total probability for two events

U2.AoS4.7

representations of compound events, the addition rule for probability, the concepts of mutually exclusive and independent events, conditional probability and the law of total probability

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