Type of event	Meaning	Examples	Probability Notation	Methods (When events occur in no particular order)	Method (when there is an order)	Formulas
Two Way Table	Venn Diagram	Tree Diagram
An event	Is a subset of the sample space	A: Failing the test	𝑃(𝐴)	A A' Totals B B' Totals	A	A P(B|A) A P(B|A) P(A) P(B ' |A) ' |A) B' B B P(B|A ' ) ' ) P(A ' ) ' ) A ' B' P(B ' |A ' ) ' |A ' )	Theoretical Probability: No. in event 𝑃(𝐴) = No. in sample space Experimental Probability: No. of favourable outcomes 𝑃(𝐴) = No. of trials
A	A'	Totals	A	A P(B|A) A P(B|A) P(A) P(B ' |A) ' |A) B' B B P(B|A ' ) ' ) P(A ' ) ' ) A ' B' P(B ' |A ' ) ' |A ' )	Theoretical Probability: No. in event 𝑃(𝐴) = No. in sample space Experimental Probability: No. of favourable outcomes 𝑃(𝐴) = No. of trials
'What might happen'	Is a subset of the sample space	A: Failing the test	𝑃(𝐴)	A A' Totals B B' Totals	B	A	A P(B|A) A P(B|A) P(A) P(B ' |A) ' |A) B' B B P(B|A ' ) ' ) P(A ' ) ' ) A ' B' P(B ' |A ' ) ' |A ' )	Theoretical Probability: No. in event 𝑃(𝐴) = No. in sample space Experimental Probability: No. of favourable outcomes 𝑃(𝐴) = No. of trials
A: Failing the test	𝑃(𝐴)	A A' Totals B B' Totals	A	A P(B|A) A P(B|A) P(A) P(B ' |A) ' |A) B' B B P(B|A ' ) ' ) P(A ' ) ' ) A ' B' P(B ' |A ' ) ' |A ' )	Theoretical Probability: No. in event 𝑃(𝐴) = No. in sample space Experimental Probability: No. of favourable outcomes 𝑃(𝐴) = No. of trials
B'	A	A P(B|A) A P(B|A) P(A) P(B ' |A) ' |A) B' B B P(B|A ' ) ' ) P(A ' ) ' ) A ' B' P(B ' |A ' ) ' |A ' )	Theoretical Probability: No. in event 𝑃(𝐴) = No. in sample space Experimental Probability: No. of favourable outcomes 𝑃(𝐴) = No. of trials
A A' Totals B B' Totals Totals
Complementary events	If A is an event, then not A (A') is the complementary event	A: Failing the test A ': Not failing the test	𝑃(𝐴) and 𝑃(𝐴')	A A' Totals B B' Totals	A' A A	A P(B|A) A P(B|A) P(A) P(B ' |A) ' |A) B' B P(B|A ' ) ' ) P(A ' ) ' ) A ' B' P(B ' |A ' ) ' |A ' )	𝑃(𝐴) 𝑃(𝐴) ) +𝑃(𝐴 = 1 𝑃(𝐴') = 1 -𝑃(𝐴)
A	A'	Totals	A' A A	A P(B|A) A P(B|A) P(A) P(B ' |A) ' |A) B' B P(B|A ' ) ' ) P(A ' ) ' ) A ' B' P(B ' |A ' ) ' |A ' )	𝑃(𝐴) 𝑃(𝐴) ) +𝑃(𝐴 = 1 𝑃(𝐴') = 1 -𝑃(𝐴)
B
'Not A'	B'
A A' Totals B B' Totals Totals
Mutually exclusive events	Two events that cannot occur in the same trial	A: Passing the test with high alcohol B: Passing the test with low alcohol	No notation	A A' Totals B B' Totals	A B	A * P(B|A) A * P(B|A) P(A) * P(B ' |A) ' |A) B' B * P(B|A ' ) ' ) P(A ' ) ' ) A ' B' * P(B ' |A ' ) ' |A ' )	Two events are mutually exclusive iff 𝑃(𝐴 ∩ 𝐵) = 0 OR 𝐵) 𝑃(𝐴) 𝑃(𝐴 ∪ = +𝑃(𝐵)
A	A'	Totals	A B	A * P(B|A) A * P(B|A) P(A) * P(B ' |A) ' |A) B' B * P(B|A ' ) ' ) P(A ' ) ' ) A ' B' * P(B ' |A ' ) ' |A ' )	Two events are mutually exclusive iff 𝑃(𝐴 ∩ 𝐵) = 0 OR 𝐵) 𝑃(𝐴) 𝑃(𝐴 ∪ = +𝑃(𝐵)
B
'Can't both happen at once'	B'
A A' Totals B B' Totals Totals
Independent events	The occurrence of A has no effect on the probability of B occurring	A: Passing the test B: Born in April	No notation	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from table then use formula. OR use meaning ' being born in April will not affect the chance that you will pass the test' use meaning ' being born in April will not affect the chance that you will pass the test'	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from venn diagram then use formula. OR use meaning ' being born in April will not affect the chance that you will pass the test'	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from tree diagram then use formula. Hint: (𝑃(𝐵) = 𝑃(𝐴 ∩𝐵)+𝑃(𝐴' ∩𝐵) OR use meaning ' being born in April will not affect the chance that you will pass the test'	Two events are independent iff ∩𝐵) 𝑃(𝐴) ×𝑃(𝐵) 𝑃(𝐴 = OR 𝑃(𝐴|𝐵) 𝑃(𝐴) =
Independent events events	'One does not affect the chance of the other'	A: Passing the test B: Born in April	A: Passing the test B: Born in April B: Born in April	No notation	OR use meaning ' being born in April will not affect the chance that you will pass the test'	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from table then use formula. OR use meaning ' being born in April will not affect the chance that you will pass the test' use meaning ' being born in April will not affect the chance that you will pass the test'	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from venn diagram then use formula. OR use meaning ' being born in April will not affect the chance that you will pass the test'	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from venn diagram then use formula. OR use meaning ' being born in April will not affect the chance that you will pass the test' OR use meaning ' being born in April will not affect the chance that you will pass the test'	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from tree diagram then use formula. Hint: (𝑃(𝐵) = 𝑃(𝐴 ∩𝐵)+𝑃(𝐴' ∩𝐵) OR use meaning ' being born in April will not affect the chance that you will pass the test'	Get 𝐵) ∩ Get 𝐵) ∩ P(A), P(B) and from tree diagram then use formula. Hint: (𝑃(𝐵) = 𝑃(𝐴 ∩𝐵)+𝑃(𝐴' ∩𝐵) OR use meaning ' being born in April will not affect the chance that you will pass the test' OR use meaning ' being born in April will not affect the chance that you will pass the test'	Two events are independent iff ∩𝐵) 𝑃(𝐴) ×𝑃(𝐵) 𝑃(𝐴 = OR 𝑃(𝐴|𝐵) 𝑃(𝐴) =	Two events are independent iff ∩𝐵) 𝑃(𝐴) ×𝑃(𝐵) 𝑃(𝐴 = OR 𝑃(𝐴|𝐵) 𝑃(𝐴) = OR 𝑃(𝐴|𝐵) 𝑃(𝐴) =

B

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A

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A

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A

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