Mathematics
Sample spaces
Class 8
Intermediate
About 15 min
Premium
Sample spaces: rolling two dice
Lay out all 36 ways two dice can land, light up the outcomes you want, and test the probability with many rolls.
Core concept
List every equally likely outcome; P(event) = favourable outcomes ÷ all outcomes
Topic: Sample spaces
In many board games two dice are rolled and their numbers added. Each die can land in 6 ways, so the pair can land in 6 × 6 = 36 ways, all equally likely. Laid out in a grid with the first die down the side and the second across the top, these 36 outcomes are the sample space. To find the probability: How likely something is to happen, from 0 (impossible) to 1 (certain). All key words of an event, count the outcomes in it and divide by 36. Some totals are much more likely than others, because there are more ways to make them.
What you will learn
- List the sample space for two dice.
- Find the probability of an event by counting favourable outcomes.
- Compare experimental results with the theoretical probability.
Before you start
- Probability as favourable ÷ all outcomes.
Materials
- Two dice
Equipment
- A tally sheet
Procedure
- Tap the event chip to choose an event; for a total, tap − or + to change it.
- Count the lit squares and read P = favourable ÷ 36.
- Tap the rolls chip to roll 36, 360 or 3600 times and compare with the theory.
- Record a total of 7, a double, at least one six, and 3600 rolls.
How this simulation is simplified
- Both dice are fair, so all 36 outcomes are equally likely.