The Open Door Web Site
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
The number of students studying Art and Biology was recorded in a Venn diagram as shown below.
(0.20 represents 20% etc.)
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)
3. Tables of outcomes
This question can also be solved using a table of outcomes
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
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
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