THE NUMBERS, EXPLAINED
How to use this calculator.
Your success probability models an informed guess. Blind guessing assumes exactly one correct option and equally likely choices. Expected values describe repeated trials; individual outcomes differ.
Start with your inputs
Enter answer options, reward if correct, penalty if wrong, success probability (%), score for skipping. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Answer options | 4 |
| Reward if correct | 1 |
| Penalty if wrong | 0.25 |
| Success probability (%) | 25 |
| Score for skipping | 0 |
A worked example
With the example inputs above, expected score if answering is 0.0625. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Expected score if answering
(25) ÷ 100 × (1)-(1-(25) ÷ 100) × (0.25) = 0.0625
Expected score if skipping
(0) = 0
Blind-guess expected score
(1) ÷ (4)-(1-1 ÷ (4)) × (0.25) = 0.0625
Break-even success probability (%)
((0)+(0.25)) ÷ ((1)+(0.25)) × 100 = 20
| Result | Example answer |
|---|---|
| Expected score if answering | 0.0625 |
| Expected score if skipping | 0 |
| Blind-guess expected score | 0.0625 |
| Break-even success probability (%) | 20 |
How this is calculated
Expected score if answering
d ÷ 100 × b-(1-d ÷ 100) × c
Expected score if skipping
e
Blind-guess expected score
b ÷ a-(1-1 ÷ a) × c
Break-even success probability (%)
(e+c) ÷ (b+c) × 100
Symbols and units
- a
- Answer options
- b
- Reward if correct
- c
- Penalty if wrong
- d
- Success probability (%)
- e
- Score for skipping
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Your success probability models an informed guess. Blind guessing assumes exactly one correct option and equally likely choices. Expected values describe repeated trials; individual outcomes differ.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Expected score if answering; Expected score if skipping; Blind-guess expected score; Break-even success probability (%). The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Your success probability models an informed guess. Blind guessing assumes exactly one correct option and equally likely choices. Expected values describe repeated trials; individual outcomes differ.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
OpenStax: algebra and proportional reasoning ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
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