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Probability
Distinguish equally likely outcomes from one actual observation.
Start with the picture
Probability describes chance under a model; it does not guarantee a short-run count or the next result.
Check with another example
1. What is the chance of an even result on a fair six-sided die?
- 1/3
- 1/2
- Even and odd must alternate
My reason
2. After five heads, what is the chance of tails on the next independent fair flip?
- Greater than 1/2
- Tails is certain
- 1/2
My reason
3. In six fair die rolls, must the face 6 occur exactly once?
- No: zero or several occurrences are possible
- Yes: its probability is 1/6
- It must occur on the last roll
My reason
Explain in your own words
Why is probability 1/2 different from a guarantee of one even result in two rolls?
Answers and reasons
1. 1/2
Three of six equally likely outcomes gives 3/6=1/2.
2. 1/2
Yes. By the stated assumptions, the next flip is independent and the faces remain equally likely.
3. No: zero or several occurrences are possible
Yes. An expected count of one is not a guarantee of exactly one occurrence.
Probability assigns a value to an event. A short run allows different sequences, including two odd outcomes.