Same Math › Grade 7 › Probability tree diagrams
What is a tree diagram in probability?
A tree diagram lists every possible outcome of two or more events. Flip a coin, then spin a spinner with red, blue and green: the coin branches into heads and tails, and each branch splits into three colors, making six outcomes. The chance of heads and red is 1 out of 6.
- First event: one branch per result.
- Second event: branches off every first branch.
- Count the ends: 2 × 3 = 6 outcomes.
Why schools teach it
It stops kids from missing outcomes
Seventh graders find probabilities of compound events using organized lists, tables and tree diagrams (7.SP.C.8). Without a system, kids often list outcomes in their heads and miss some, especially mixed ones like tails then red.
The tree also shows why you multiply: two choices, each splitting three ways, make 2 × 3 outcomes.
At the kitchen table
What to say, and what to skip
Say this
What can happen first?
For each of those, what can happen next?
How many paths are there in all?
How many of those paths match what we want?
That's the top of the fraction.
Skip this
- Listing outcomes in your head.Draw the tree so none get lost.
Heads and red is 1/2 + 1/3.
For both to happen, multiply: 1/2 × 1/3 = 1/6.- Assuming outcomes are equally likely.Only if every branch is equally likely, like a fair coin.
See it in action
Two coin flips: chance of one head and one tail
Draw the tree
HH, HT, TH, TTCount the outcomes that match
HT and TH: 2Write the probability
2 out of 4 = 1/2
Kids often say 1/3, thinking HT and TH are the same. The tree shows they're different paths.
Free practice sheet
Make a tree diagram sheet
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Parents also ask
What's a sample space?
The list of all possible outcomes. The ends of the tree are the sample space.
When do you multiply probabilities?
For independent events that both happen, like heads and red.
Can tree diagrams have three levels?
Yes, like three coin flips (8 outcomes). They grow quickly.
Is a table the same thing?
For two events, a table shows the same outcomes. Trees work better for three or more.