Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

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

Conditional probability is the probability of an outcome occurring given that another event has occurred.

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 Venn 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

Event A and event B are mutually exclusive events. Which of these statements are correct?

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

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

The diagram shows the number of outcomes for two events A and B. The values of P(A | B) and P(A | B') show that 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 {{}}.

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

Taking a counter at random from a box, replacing it and then taking another

Taking a counter at random from a box, keeping it and then taking another

Select the example of events which are not independent.

The table shows the types of marble in a bag. Match each event to its probability.

A marble is taken at random from a box of marbles. Alex works out that P(swirl given it is blue) = P(swirl). This shows the event 'has a swirl' is __________ of the event 'blue marble'.

A 10-sided die with integers from 1 to 10 written on it is rolled once. Select the pair of mutually exclusive events.

A deck of cards has a number on it (either prime or non-prime), and a symbol (a circle, square, or wave). A card is selected at random from the deck. Find P(non-prime | wave).

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