The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.

Event A is independent of event B if the probability of event A occurring is not affected by whether or not event B occurs.

Mutually exclusive events have no outcomes in common.

Conditional probability in a tree diagram

Maths

In this unit, pupils use their knowledge of calculating theoretical probabilities and extend this understanding to calculating conditional probabilities using all of the representations encountered in the prior unit.

Conditional probability

Two events A and B are independent. This means that...

Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school. Match each value to its probability.

Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school.  P(Sofia is late for school) = {{ }}.

Here is a general probability tree. Which of these probabilities give the probability of the highlighted events? 

One marble is taken at random from a bag of 7 purple and 5 green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows these two events. Find the value of $$x$$.

One marble is taken at random from a bag of purple and green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows the two events. Find P(both marbles are green).

Event A and event B are mutually exclusive events. The P(A and B) is {{}}.

From the frequency Venn diagram, P(A | B) = {{}}. Write your answer as a decimal.

From the frequency Venn diagram, P(A | B') = {{ }}. Write your answer as a decimal.

The diagram shows the number of outcomes for two events A and B. The events A and B are __________ events.

Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) =  $$3 \over 10$$. The value of $$x$$ is {{}}.

Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) =  $$3 \over 10$$. The value of $$y$$ is {{}}.

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