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3. Tree Diagrams
Definition: A tree diagram displays all possible outcomes of a series of events, showing
probabilities along the branches.
Example: If you pick a fruit from a basket containing apples (A) and bananas (B):
First Pick:
A (0.5)
B (0.5)
Second Pick (with replacement):
From A: A (0.5) or B (0.5)
From B: A (0.5) or B (0.5)
Tree Diagram:
First Pick
/ \
A (0.5) B (0.5)
/ \ / \
A B A B
(0.5) (0.5) (0.5) (0.5)
Calculating Probabilities:
Probability of picking an Apple both times:
P(A,A) = 0.5×0.5 = 0.25
Probability of picking an Apple first and a Banana second:
P(A,B) = 0.5×0.5 = 0.25
(Sample Space Diagrams are useful for visualizing all outcomes. Venn Diagrams are
effective for understanding the relationships between two events. Tree Diagrams are
helpful for displaying outcomes of sequential events and calculating combined
probabilities.)
(Here is an example of a question that you might face in the exams)