Tree diagrams
A branching picture showing all possible outcomes of events in order. Probabilities go on the branches and you multiply along them.
Last updated
Analogy
Like a map of every route you could take at each junction.
Example
P(red, red) = 3/5 x 2/4= 6/20 = 3/10
In practice
Used to plan for outcomes like picking sweets from a bag without putting them back.
Practice
Flashcards
- A bag has 3 red and 2 blue. Pick two red without replacement.3/5 x 2/4 = 3/10.
Interview questions
- A bag has 3 red and 2 blue counters. Two are taken without replacement. Find the probability both are red and explain.
- First red: 3/5
- Second red: 2/4 as one red is gone
- Multiply along the branch
- 3/5 x 2/4 = 6/20 = 3/10
Questions people ask
What changes when there is no replacement?
The total number of items goes down after the first pick, so the second probabilities change. After taking a red from 3 red and 2 blue, 4 items remain with 2 red. The second red is 2/4, not 3/5. With replacement, the probabilities stay the same on every branch because the total never changes.
How do you find the chance of several outcomes on a tree diagram?
Multiply along each branch that leads to a wanted outcome, then add the results of the different branches. Multiplying gives the chance of a path, and adding combines paths that both count. For example, the chance of exactly one red adds the red-then-blue and blue-then-red branches together, after multiplying each one.