Two labels need not have equal probability. In this hypothetical example, three distinguishable tokens are equally likely to be selected: A1, A2 and B1. Each token has probability 1/3. The printed letters group the tokens; they do not describe equally sized groups.
List the outcomes before grouping the labels
The complete sample space is:
| Token | Printed label | Probability |
|---|---|---|
| A1 | A | 1/3 |
| A2 | A | 1/3 |
| B1 | B | 1/3 |
There are three equally likely elementary outcomes, not two. The event “label A” contains the set {A1, A2}, while the event “label B” contains {B1}. Therefore:
P(A) = 2/3
P(B) = 1/3
Events group outcomes; counting requires equal likelihood. Reference: OpenStax terminology for sample spaces and events.
Why counting label names gives the wrong ratio
If someone counts only the visible names, they see A and B and may write 1/2 for each. That calculation silently changes the sample space from three tokens to two labels. It also discards multiplicity: label A appears on two distinct equally likely tokens, whereas label B appears on one.
You can check the grouping by assigning three counters, one per token: two go to A and one to B. Moving both A counters into one labelled box does not turn them into a single counter. The two groups still exhaust all three possibilities.
What changes when the tokens change?
Consider a second explicitly hypothetical model with only two distinguishable tokens: A1 and B1. Keep the same uniform-token assumption: each token is equally likely. Now the sample space is {A1, B1}. Label A contains one outcome and label B contains one outcome, so:
P(A) = 1/2 and P(B) = 1/2.
The ratio changed because the list now contains one token per label. Before assigning probabilities to a screen's categories, identify the underlying outcomes and whether they are equally likely. Merely seeing two names cannot establish that information. This model is an illustration, not evidence about a real game's mechanism.
For a different question about interpreting past observations, see our history-screen reading note. The hypothetical counts above are not observed results.