Further Venn Diagrams

What do you mean by further Venn diagrams?

The Venn diagrams used here are no more complicated than those in the first Venn Diagrams revision note, however
- questions may use set notation as well, or alongside contextual questions
- there may be more detailed use of conditional probability
- mutually exclusive, three events and other unusual Venn diagram setups may be involved

2-3-3-cie-fig0-special-venn

How do I solve conditional probability problems using Venn diagrams?

Interpreting questions in terms of AND ( $\cup$ ), OR ( $\cap$ ), complement ( ‘ ) and
“given that” ( | )
Use mini-Venn diagrams to sketch and shade the regions you are dealing with – use different colours if available or different styles of shading if not
- Shading can help you see the answer

since $P (A | B) = \frac{P (A \cap B)}{P (B)}$ shade B first, then shade $A \cap B$

the answer will then be $\frac{" double shading "}{" single shading "}$

plx9zFR~_3-2-2-fig1-set-notation-examples

Worked example

Three events, $A, B$ and $C$ are such that

events $A$ and $C$ are mutually exclusive

$P (A \cap B) = 0.2 P (B \cap C) = 0.3 P ((A \cup B \cup C)') = 0.1 P (B) = 0.7 P (A') = 0.75 .$

Find

(i)

P (A | B)

(ii)

P (A' | C')

(iii)

P (C | (A \cup B)')

2-3-3-ciie-fig2-we-solution_part1

2-3-3-ciie-fig2-we-solution_part2

Examiner Tip

Although very versatile, Venn diagrams may not always be the best option
- use a tree diagram if one event follows another

e.g. two beads drawn from a bag without replacement

- use a two-way table for showing how many items/people are in associated categories
  e.g. A school year group split by gender selecting which sport they wish to play

Further Venn Diagrams (CIE AS Maths: Probability & Statistics 1)

Revision Note

What do you mean by further Venn diagrams?

How do I solve conditional probability problems using Venn diagrams?

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1. Data Presentation & Interpretation

1.1 Statistical Measures

1.1.1 Basic Statistical Measures

1.1.2 Frequency Tables

1.1.3 Standard Deviation & Variance

1.1.4 Coding

1.2 Representation of Data

1.2.1 Data Presentation

1.2.2 Stem and Leaf Diagrams

1.2.3 Box Plots & Cumulative Frequency

1.2.4 Histograms

1.3 Working with Data

1.3.1 Interpreting Data

1.3.2 Skewness

2. Probability

2.1 Basic Probability

2.1.1 Calculating Probabilities & Events

2.1.2 Venn Diagrams

2.1.3 Tree Diagrams

2.2 Permutations & Combinations

2.2.1 Arrangements & Factorials

2.2.2 Permutations

2.2.3 Combinations

2.3 Further Probability

2.3.1 Set Notation & Conditional Probability

2.3.2 Further Tree Diagrams

2.3.3 Further Venn Diagrams

2.3.4 Probability Formulae

3. Statistical Distributions

3.1 Probability Distributions

3.1.1 Discrete Probability Distributions

3.1.2 E(X) & Var(X) (Discrete)

3.2 Binomial & Geometric Distribution

3.2.1 The Binomial Distribution

3.2.2 Calculating Binomial Probabilities

3.2.3 The Geometric Distribution

3.3 Normal Distribution

3.3.1 The Normal Distribution

3.3.2 Standard Normal Distribution

3.3.3 Normal Distribution - Calculations

3.3.4 Finding Sigma and Mu

3.4 Working with Distributions

3.4.1 Modelling with Distributions

3.4.2 Normal Approximation of Binomial

Author: Paul