Tree Diagram Word Problems Worksheets

All 12 blanks on the diagram

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Coin flips 2

1/4 Multiply along the path: 1/2 × 1/2 = 1/4.
1/2 Add the paths: 1/4 + 1/4 = 2/4 = 1/2.

Two marbles 4

4/5 Of the 5 left, 4 are red: 4/5.
2/5 Multiply along the path: 2/3 × 3/5 = 6/15 = 2/5.
1/15 Multiply along the path: 1/3 × 1/5 = 1/15.
7/15 Add the paths: 2/5 + 1/15 = 6/15 + 1/15 = 7/15.

Rain and bus 6

0.7 A fork adds to 1: 1 − 0.3 = 0.7.
0.6 A fork adds to 1: 1 − 0.4 = 0.6.
0.9 A fork adds to 1: 1 − 0.1 = 0.9.
0.12 Multiply along the path: 0.3 × 0.4 = 0.12.
0.07 Multiply along the path: 0.7 × 0.1 = 0.07.
0.19 Add the paths: 0.12 + 0.07 = 0.19.

How this list was compiled: Own work: the marble and bus problems and their numbers were written for this sheet; two flips of a coin is the usual first example and is on both pages named here. The method was read on 2026-10-03 in two places. (1) Wikipedia, English edition, Tree diagram (probability theory), https://en.wikipedia.org/wiki/Tree_diagram_(probability_theory): a tree may show independent events, such as coin flips, or conditional probabilities, as in drawing without replacing; each set of sibling nodes is a partition of the parent event, exclusive and exhaustive, so the branches from one point add to 1; the probability of a series of events is the product of the probabilities along it; probabilities that lie on the same branch are multiplied and those that do not are added. (2) Math is Fun, Probability Tree Diagrams, https://www.mathsisfun.com/data/probability-tree-diagrams.html: the two tosses of a coin; probabilities are multiplied along the branches and added down the columns; the end probabilities add to 1. No answer is typed by hand: every blank is worked out with exact fractions by the program that draws the sheet, and again by a second program. Licence: own work

The drawing: Drawn for this site on 2026-10-03 by script from the answer table in the dataset. Own work. Licence: own work

How it works

These tree diagram word problems worksheets put three probability trees on one sheet: two coin flips, two marbles taken from a bag without putting the first one back, and rain with a late bus. Fill in the numbered blanks.

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Read a tree in three moves

The branches from one point add to 1, so a missing branch is 1 minus the other. Multiply the probabilities along a path to get the chance of that pair of outcomes. When more than one path fits the question, add those paths.

When the first marble is kept out

After one marble is taken, 5 are left, so the second fractions depend on which marble came out. After a red, 3 of the 5 are red. After a blue, 4 of the 5 are red.

The four paths of a tree add to 1.

Questions and answers

How do you solve a probability tree diagram word problem?

Write each outcome at the end of a branch and its probability on the branch. Multiply along a path for the chance of that pair of outcomes, then add the paths that fit the question.

Do you multiply or add on a tree diagram?

Both. Probabilities along the same path are multiplied. The results of different paths are added: one head and one tail can come as H then T or as T then H, so those two paths are added.

What does without replacement change on a tree diagram?

The second set of branches depends on the first result. With 4 red and 2 blue marbles, taking a red leaves 5 marbles, 3 of them red, so the next red branch is 3/5.

Does the worksheet come with answers?

Yes. Print the answer key gives the numbered sheet with the answer to every blank listed under it. On screen, Quiz yourself on this worksheet checks each answer as you give it.