Definition
Theoretical probability
Theoretical probability is probability worked out from a mathematical model of possible outcomes.
Continue from this idea into connected AXIO math.
Model first, results later: work from what could happen and how likely it is.
Boundary: For a spinner with unequal sections, counting section names is not enough; the model must use the sections’ actual sizes or assigned probabilities.
What it means
Use how the chance setup is built, not a record of what already happened. First describe the possible outcomes and how likely the model says each one is. If they are all equally likely, count the outcomes you want and divide by the total number of outcomes.
Remember it
Model first, results later: work from what could happen and how likely it is.
Example
A bag has 2 red counters and 3 yellow counters, and each counter is equally likely to be drawn. The theoretical probability of red is 2/5 because 2 of the 5 equally likely counters are red.
Watch for
For a spinner with unequal sections, counting section names is not enough; the model must use the sections’ actual sizes or assigned probabilities.
Common mix-up
Theoretical probability comes from a model. Experimental probability comes from observed results in trials.
Exact meaning
Theoretical probability is the probability predicted by a mathematical model of the possible outcomes. When outcomes are equally likely, it equals the number of favourable outcomes divided by the total number of outcomes; otherwise, use the probabilities assigned by the model.