Listing Outcomes and Expected Frequency

Sample Space Diagrams

Sample space diagrams can be used to list all outcomes.

Example: A spinner has three sides numbered 1, 2 and 3. It is spun twice and the results are added together. What is the probability of spinning a total of 5.

Make a sample space diagram showing all the outcomes like this:

sample space diagram

This makes it easy to see there are 9 possible outcomes and what they all are. This in turn makes it easier to work out the probability asked for:

P(total = 5) = ways to score 5 / total possible outcomes = 2/9 

Expected Frequency

This just means estimating how many times an event will happen when you carry out an experiment a certain number of times.

Expected Frequency = Probability x Number Of Trials

So if you throw a fair coin 50 times:

Expected number of heads = 0.5 x 50 = 25