8.2

Combined events

Cambridge IGCSE Mathematics (0580)  · Unit 8: Probability  · 10 flashcards

Combined events is topic 8.2 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 8 — Probability , alongside Basic probability and Venn diagrams.  In one line: Independent events are events where the outcome of one does not affect the outcome of the other.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 10 flashcards — 4 definitions and 2 key concepts — covering the precise wording mark schemes reward.  Use the 4 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

'independent events' in probability and provide an example

Independent events are events where the outcome of one does not affect the outcome of the other.

Example: Flipping a coin and rolling a dice are independent events.

Questions this Combined events deck will help you answer

Definition Flip

Define 'independent events' in probability and provide an example.

Answer Flip

Independent events are events where the outcome of one does not affect the outcome of the other.

Example: Flipping a coin and rolling a dice are independent events.
Definition Flip

Define 'dependent events' in probability and provide an example.

Answer Flip

Dependent events are events where the outcome of one affects the outcome of the other.

Example: Drawing two cards from a deck without replacement.
Definition Flip

Define 'mutually exclusive events' in probability and provide an example.

Answer Flip

Mutually exclusive events are events that cannot occur at the same time.

Example: Rolling a 1 and rolling a 6 on a single roll of a die are mutually exclusive.
Key Concept Flip

Explain how to use a tree diagram to calculate the probability of combined events.

Answer Flip

A tree diagram visually represents probabilities of different outcomes. Multiply probabilities along each branch to find the probability of a specific sequence of events.

Key Concept Flip

State the 'AND rule' for independent events and provide a calculation example.

Answer Flip

The AND rule states that P(A and B) = P(A) * P(B) for independent events.

Example: P(rolling a 4 on a die AND flipping heads) = (1/6) * (1/2) = 1/12.
Key Concept Flip

State the 'OR rule' for mutually exclusive events and provide a calculation example.

Answer Flip

The OR rule states that P(A or B) = P(A) + P(B) for mutually exclusive events.

Example: P(rolling a 1 or 2 on a die) = (1/6) + (1/6) = 1/3.
Key Concept Flip

A bag contains 5 red and 3 blue balls. Two balls are drawn without replacement. What is the probability of drawing a red ball, then another red ball?

Answer Flip

P(Red, then Red) = (5/8) * (4/7) = 20/56 = 5/14. The probability changes on the second draw because the first ball is not replaced, creating a dependent event.

Key Concept Flip

Explain the difference between drawing 'with replacement' and 'without replacement' and its impact on probabilities.

Answer Flip

With replacement means the item is returned after selection, keeping probabilities constant. Without replacement means the item is not returned, altering probabilities for subsequent selections.

Definition Flip

Define 'conditional probability' and provide a scenario where it applies.

Answer Flip

Conditional probability is the probability of an event A occurring, given that event B has already occurred. Scenario: What is the probability that it will rain tomorrow, given that it is cloudy today?

Key Concept Flip

The probability it will rain today is 0.3. The probability the baseball game is cancelled if it rains is 0.7. What is the probability that it rains AND the baseball game is cancelled?

Answer Flip

P(Rain and Cancelled) = P(Rain) * P(Cancelled | Rain) = 0.3 * 0.7 = 0.21. We use the AND rule with conditional probability.

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8.1 Basic probability 8.3 Venn diagrams

Key Questions: Combined events

Define 'independent events' in probability and provide an example.

Independent events are events where the outcome of one does not affect the outcome of the other.

Example: Flipping a coin and rolling a dice are independent events.
Define 'dependent events' in probability and provide an example.

Dependent events are events where the outcome of one affects the outcome of the other.

Example: Drawing two cards from a deck without replacement.
Define 'mutually exclusive events' in probability and provide an example.

Mutually exclusive events are events that cannot occur at the same time.

Example: Rolling a 1 and rolling a 6 on a single roll of a die are mutually exclusive.
Define 'conditional probability' and provide a scenario where it applies.

Conditional probability is the probability of an event A occurring, given that event B has already occurred. Scenario: What is the probability that it will rain tomorrow, given that it is cloudy today?

More topics in Unit 8 — Probability

Combined events sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

8.1 Basic probability

9 flashcards
8.3 Venn diagrams

10 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

combined events independent dependent mutually exclusive tree diagram probability tree AND rule OR rule multiply add without replacement with replacement conditional probability

Key terms covered in this Combined events deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

'independent events' in probability and provide an example
'dependent events' in probability and provide an example
'mutually exclusive events' in probability and provide an example
'conditional probability' and provide a scenario where it applies

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How to study this Combined events deck

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