Conditional probability specifically concerns how one event changes the likelihood of another.

Dependent events mean the outcome of the first event affects the probability of the second.

Dependent events require replacement of items.

Independent events have probabilities that change based on previous outcomes.

Independent events always result in a lower total probability.

Removing an item without replacement changes the total number of available outcomes for the next draw.

The student forgot that the deck size decreases.

The student assumed the colours of the cards remain constant.

The student ignored the total number of suits.

The student failed to use a probability tree diagram.

Tree diagrams for dependent events must show updated probabilities after the first branch.

The probabilities on the branches must be updated to reflect the new sample space.

The probabilities on the branches remain the same as the first set.

The sum of all branches must equal 2.

The branches should only show the final outcome.

AQA GCSE Maths

Conditional probability

AQA GCSE Maths revision on Conditional probability. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.

Sample questions (3 of 16)

Question 1

When calculating the probability of two events occurring, what is the primary difference between independent and dependent events?
- A) Dependent events require replacement of items.
- B) Independent events have probabilities that change based on previous outcomes.
- C) Dependent events mean the outcome of the first event affects the probability of the second.
- D) Independent events always result in a lower total probability.
Show answer

Answer: Dependent events mean the outcome of the first event affects the probability of the second.

In probability, independence means the occurrence of one event has no influence on another. When events are dependent, the sample space or the composition of the set changes after the first event, which is the core concept of conditional probability.
Question 2

A student claims that drawing two cards from a deck without replacement is an independent process. What is the fundamental error in this reasoning?
- A) The student forgot that the deck size decreases.
- B) The student assumed the colours of the cards remain constant.
- C) The student ignored the total number of suits.
- D) The student failed to use a probability tree diagram.
Show answer

Answer: The student forgot that the deck size decreases.

Because the first card is not put back, the denominator for the second probability must change. This change in the available pool of items makes the second event dependent on the result of the first.
Question 3

If you are given a tree diagram for dependent events, what must be true about the branches following the first event?
- A) The probabilities on the branches remain the same as the first set.
- B) The probabilities on the branches must be updated to reflect the new sample space.
- C) The sum of all branches must equal 2.
- D) The branches should only show the final outcome.
Show answer

Answer: The probabilities on the branches must be updated to reflect the new sample space.

In conditional probability, the second stage of a tree diagram represents the state of the system after the first event has occurred. Therefore, the fractions must reflect the reduced or altered totals resulting from that first action.

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