Probability Tree Diagram

Updated 01 Oct 2026

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What it is
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  represents sequential outcomes using branches labeled with conditional probabilites
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Rules
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  outgoing branch probabilities at each reachable node sum to $1$
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  multiply along a path to obtain its joint probability
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  add probabilities of mutually exclusive terminal paths to obrain an event probability
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Example
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  Draw twice from $3$ red and $7$ blue objects.
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  With replacement: $P(RR)=0.09$ , $P(RB)=0.21$ , $P(BR)=0.21$ , $P(BB)=0.49$ .
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  Without replacement: $P(RR)=1/15$ , $P(RB)=7/30$ , $P(BR)=7/30$ , $P(BB)=7/15$ .
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  Thus, without replacement, $P(\text{different colors})=7/15$ .

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