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Sample spaces and Venn diagrams
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Listing every possible outcome in an organised way makes probabilities much easier to find.
Sample spaces
A sample space lists every possible outcome. For two events, use a grid.
Roll two dice and add: there are 6 Γ 6 = 36 equally likely outcomes. Six of them make 7, so P(total 7) = 636 = 16.
Roll two dice and add: there are 6 Γ 6 = 36 equally likely outcomes. Six of them make 7, so P(total 7) = 636 = 16.
Venn diagrams and sets
ΞΎ is the universal set: everything being considered.
A β© B (A intersection B): in A and B, the overlap.
A βͺ B (A union B): in A or B or both.
Fill a Venn diagram from the overlap outwards.
A β© B (A intersection B): in A and B, the overlap.
A βͺ B (A union B): in A or B or both.
Fill a Venn diagram from the overlap outwards.
Mutually exclusive events
Events that cannot happen at the same time are mutually exclusive, such as rolling a 2 and rolling a 5 with one dice.
For mutually exclusive events, P(A or B) = P(A) + P(B).
For mutually exclusive events, P(A or B) = P(A) + P(B).
30 students: 18 play football, 12 play tennis and 5 play both. How many play neither?
- Football only: 18 β 5 = 13. Tennis only: 12 β 5 = 7
- In the circles: 13 + 5 + 7 = 25
- Neither: 30 β 25
Answer: 5
List outcomes systematically in a grid or Venn diagram. β© means and (the overlap), βͺ means or. Start a Venn diagram with the overlap.
The interactive lesson includes the diagrams for this topic.
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