Probability tree diagram
Bag: 3 red, 2 blue
Red 3/5
Red 2/4: red, red = 3/10
Blue 2/4: red, blue = 3/10
Blue 2/5
Red 3/4: blue, red = 3/10
Blue 1/4: blue, blue = 1/10
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What a probability tree diagram is
“In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such as a set of coin flips) or conditional probabilities (such as drawing cards from a deck, without replacing the cards).”
Types of tree diagram
When to use a probability tree diagram
Maths
Multiply along the branches to get each ending: 3/5 times 2/4 gives 3/10 for red, then red.
Studying
Draw one for any “without putting it back” question, so the second draw's chances are clear.
Exam revision
A quick check on an exam answer: all the endings should add up to 1.
How to make a probability tree diagram
- 1The bagBag: 3 red, 2 blue
- 2First marbleBag: 3 red, 2 blueRed 3/5Blue 2/5
- 3Second marbleBag: 3 red, 2 blueRed 3/5Red 2/4: red, red = 3/10Blue 2/4: red, blue = 3/10Blue 2/5Red 3/4: blue, red = 3/10Blue 1/4: blue, blue = 1/10
Helpful resources
Questions
- How do I get the chance of each ending?
The probability that the series of events leading to a particular node will occur is equal to the product of that node and its parents' probabilities.
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