8.2

Combined events

10 flashcards to master Combined events

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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?

About Combined events (8.2)

These 10 flashcards cover everything you need to know about Combined events for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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