Mr. Rogers - AP Statistics

The Relationship of Venn Diagrams to Tree Diagrams--Conditional Events

Any probability problem that can be represented by a Venn diagram can also be represented by a tree diagram and vice versa. The diagrams at right are set up for conditional events, but will will look very similar for independent events.

Note that specific leaves on the tree correspond to specific areas of the Venn diagram. This is true for both independent and conditional events.

For Conditional Events:

1. P(A∩B) = P(A) • P(B|A)
2. P(AUB) = P(A) + P(B) - [P(A) • P(B|A)]

Example:

• P(A)      =  49 %, probability of being male
• P(B|A)  =  5 %, probability of wearing a pink dress given being male
• P(A^c)     =  51 %, probability of being female
• P(B|A^c) =  20 % probability of wearing a pink  dress given being female

1. P(A∩B) = 2.45 %, probability of wearing a pink dress and being a male
2. P(AUB) = 59.2 %, probability of being a male or wearing a pink dress

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