Sample Space Diagram Worksheet – Coins and Dice, With Key

All 18 blanks on the diagram

Show the list

Complete the diagram 8

TH Row T, column H: tails first, then heads.
H6 Row H, column 6: heads and a 6.
T4 Row T, column 4: tails and a 4.
2 Row 1 plus column 1: 1 + 1 = 2.
5 Row 2 plus column 3: 2 + 3 = 5.
7 Row 3 plus column 4: 3 + 4 = 7.
9 Row 5 plus column 4: 5 + 4 = 9.
12 Row 6 plus column 6: 6 + 6 = 12.

Use the diagram 10

1/4 1 of the 4 outcomes is HH: 1/4.
1/2 2 of the 4 outcomes are HT and TH: 2/4 = 1/2.
3/4 3 of the 4 outcomes have a head: 3/4.
1/12 1 of the 12 outcomes is T6: 1/12.
1/3 4 of 12 outcomes have a 5 or 6: 1/3.
1/6 6 of the 36 cells hold 7: 6/36 = 1/6.
1/36 1 of the 36 cells holds 12: 1/36.
1/9 4 of the 36 cells hold 5: 4/36 = 1/9.
5/36 5 of the 36 cells hold 8: 5/36.
5/18 10 of the 36 cells hold 9 or more: 10/36 = 5/18.

How this list was compiled: Own work: the three diagrams and their questions are the site's. The term and the method were read on 2026-10-03. (1) Wikipedia, English edition, Sample space, https://en.wikipedia.org/wiki/Sample_space: the sample space holds all possible outcomes; for tossing two coins it is HH, HT, TH, TT, where HT means heads on the first coin and tails on the second; two six-sided dice give 36 equally likely ordered pairs; when every outcome is equally likely, the probability of an event is the number of outcomes in the event over the number of outcomes in the sample space. (2) Math is Fun, Probability: Types of Events and Activity pages, https://www.mathsisfun.com/data/probability.html: the sample space is all the possible outcomes of an experiment; two dice have 36 sample points. (3) For the name sample space diagram, two school textbooks read by full-text search: a foundation mathematics textbook of 2010, https://archive.org/details/newgcsenathsfoun0000unse (the outcomes of a combined event are shown with a sample space diagram, as when two dice are thrown), and an 11+ mathematics book of 2002, https://archive.org/details/11maths0000curr (a sample space diagram can be drawn to represent possible outcomes). No answer is typed by hand: every cell and every count is worked out 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

This sample space diagram worksheet has three grids of outcomes: two coins, a coin and a die, and the totals of two dice. Fill in the empty cells, then count cells to write each probability as a fraction.

Read the full guide

Complete the diagram

A sample space diagram shows every outcome of two things that happen together. Each cell joins its row heading to its column heading: row T and column H make TH. On the dice grid the two numbers are added, so row 3 and column 4 make 7.

Use the diagram

When every outcome is equally likely, count the cells that fit the event and divide by the number of cells. Six of the 36 dice cells hold a total of 7, so the probability is 6/36, which is 1/6.

HT and TH are different outcomes: the first letter is the first coin.

Questions and answers

What is a sample space diagram?

A table that shows every possible outcome of two events together, such as two coins or two dice. One event's results run down the side, the other's across the top, and each cell is one outcome.

How many outcomes are there when two dice are rolled?

Thirty-six. Each of the 6 numbers on the first die can come with each of the 6 on the second, so the grid has 6 rows and 6 columns.

How do you find a probability from a sample space diagram?

Count the cells that fit the event, then divide by the total number of cells. This works when every outcome is equally likely, as with fair coins and dice.

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.