Tree and Venn Diagrams for Probability

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Tree diagram

A graph whose branches show possible results at successive stages of an experiment.

With replacement

Returning a selected item before the next draw, keeping the collection's composition unchanged.

Without replacement

Not returning a selected item before the next draw, changing the collection's composition.

Intersection of two events

The outcomes that belong to both events, denoted $A\cap B$.

Union of two events

The outcomes that belong to at least one event, denoted $A\cup B$.

Quiz questions

1. Let $A=\{1,2,3,4,5,6\}$ and $B=\{6,7,8,9\}$. What is $A\cap B$?Answer: $\{6\}$
2. If $P(A)=0.40$, $P(B)=0.50$, and $P(A\cap B)=0.05$, what is $P(A\cup B)$?Answer: $0.85$
3. If $P(A\cap B)=0.05$ and $P(B)=0.50$, what is $P(A\mid B)$?Answer: $0.10$
4. In a standard Venn diagram, what does the rectangle represent?Answer: The sample space of all possible outcomes.
5. For two coin flips, let $A$ mean tails on the first flip and $B$ mean tails on the second. Which outcome is in neither event?Answer: $HH$