Free · Mathematics models
Rare-Event Expected Counts and Exposure
Explore expected counts and exposure duration under an entered rare-event rate.
- Formula & worked example
- Private in your browser
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
Eight active hours per day, one event per second and ten days give 288,000 events. With a hypothetical probability of one in a million per event, the expected count is 0.288, not a guarantee of an outcome.
Expected outcomes = exposure seconds×events per second×event probability. Exposure for an expected count is the count divided by the expected-outcome rate.
Worked example
Enter these known values and leave the other values blank.
- Hours awake per day
- 8 hrs
- Frequency of events
- 1 per sec
- Time period
- 10 days
- In the next...
- 10 days
- To experience....
- 1 miracle(s)
- you will experience
- 0.29 miracle(s)!
- you need to wait
- 35 days
- Miracle: 1 event in
- 1000000 events
- Number of miracles
- 0.3
- Events experienced
- 288000
Assumptions and limitations
- The captured default probability is one in a million per event; it is a hypothetical input, not an empirical prediction about unusual experiences.
- Hours are active exposure per day. The first section allows a chosen event frequency; the later sections assume one event per second and eight active hours per day.
- Expected counts are averages over repeated exposure. Reaching an expected count of one is not a guarantee of one outcome, and dependence between events is omitted.
- Clear the unknown numeric field before solving a supported inverse.
Common questions
What does this scenario assume?
The captured default probability is one in a million per event; it is a hypothetical input, not an empirical prediction about unusual experiences.
What does the result leave out?
Expected counts are averages over repeated exposure. Reaching an expected count of one is not a guarantee of one outcome, and dependence between events is omitted.
References
Model input requirements: Per-event probability cannot exceed one. Daily active exposure cannot exceed 24 hours.