Stats YEAR 2 Chapter 2

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Set Notation/Venn Diagrams

Dependant/Independant Venn diagrams

We use set notation to describe the events within a sample space. This helps when dealing with probabilities.

For example:

The event A and B can be written as A∩B (pronounced A intersection B)

The event A or B can be written as A∪B (pronounced A Union B)

The event of not A can be written as A' (pronounced the complement of A)

The ξ symbol is used to represent the whole sample space for all Venn diagrams

Mutually Exclusive Venn diagrams

Because mutually exclusive Venn diagrams do not touch, then they will not have an intersection, meaning their intersection will be an empty space. This means that the A∩B (the A intersection B) for mutually exclusive events will = ∅ (the empty space)

The ξ symbol is used to represent the whole sample space for all Venn diagrams

THE OVERALL PROBABILITY OF ANY VENN DIAGRAM IS EQUAL TO 1

n(X) represents the number of outcomes in the event X

p(X) represents the probability that the event X occurs

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Conditional Probability

Basics For Conditional Probability.

The notation used for conditional probability being p(A|B) which means the probability of an event ( A ) happening , given that another ( B ) has already occurred.

p(A'|B) this would mean the probability of event (A) not happening given that event (B) has happened

For independant events, p(A|B) = p(A|B') = p(A)

, p(B|A) = p(B|A') = p(B)

This is the formula used for calculating conditional probability (below). You always divide by the probability which is given for example,

1) Calculate the probability of A given B 2) Calculate the probability of B given A

p(A|B) = p(A∩B) p(A|B) = p(B∩A)

p(B) p(A)

You always divide by the probability which is given (Example above)

Probability Formulae

p(A∪B) = p(A) + p(B) - p(A∩B)

This is used when we add probabilities in the A and B sets in Venn diagrams, we would have to substract the intersection otherwise we would be double counting it.

2 Way Tables

https://www.pearsonactivelearn.com/ebook.asp?id=NzAzNzMzfGJvb2t8Mjd8MA==

Exercise 2B

Venn Diagrams

https://www.pearsonactivelearn.com/ebook.asp?id=NzAzNzMzfGJvb2t8Mjd8MA==

Exercise 2C

Tree diagrams

https://www.pearsonactivelearn.com/ebook.asp?id=NzAzNzMzfGJvb2t8Mjd8MA==

Exercise 2E

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FULL LAWS OF PROBABILITY

If the events are independant, then:

p(A∩B) = p(A) x p(B) (This is the test for independance)

p(A|B) = p(A)

If the events are mutually exclusive, then:

p(A∩B) = 0 (This is because they do not intersect on mutually exclusives)

p(A∪B) = p(A) + p(B)

Probability Formula/Addition Forumla:

p(A∪B) = p(A) + p(B) - p(A∩B)

p(A∩B) = p(A) + p(B) - p(A∪B)

This is used when we add probabilities in the A and B sets in Venn diagrams, we would have to sub tract the intersection otherwise we would be double counting it.

(Provided they're not mutually exclusive)

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iMPORTANT TIPS