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Logic, Sets and Probability

Calculating Probability without the Formula

1. Using Venn Diagrams and Tree diagrams to solve probability questions

There are many probability questions that can be solved using either a table of outcomes, Venn diagrams or Tree diagrams

 

Venn Diagrams

Examples :

The number of students studying Art and Biology was recorded in a Venn diagram as shown below.

(0.20 represents 20% etc.)

image01

 

image02

 

2. Tree Diagrams

Example : Draw a tree diagram that could be used to calculate the probabilities of getting a six when rolling a dice twice (same as rolling two dice once)

image03

 

image04

 

3. Tables of outcomes

This question can also be solved using a table of outcomes

image05

We can see there are 36 outcomes and we just have to count the number of, for example at least one six see above highlighted in red there are 1136

The table of outcomes is also useful for solving problems like the following:

What is the probability of having a score less than five on rolling two dice? See the numbers highlighted in blue equation

 

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