Probability of @@S@@ successes on @@N@@ draws
| Probability for 1 draw | @@p@@ | % | |
|---|---|---|---|
| Maximum number of draws | @@N@@ | ||
| Selected value for first chart | @@N@@ | ||
| Selected value for second chart | @@S@@ | ||
@@\mathrm{P}(S\text{ successes on }N\text{ draws})@@
| N\S | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 100 | ||||||||||
| 1 | 50 | 50 | |||||||||
| 2 | 25 | 50 | 25 | ||||||||
| 3 | 12.5 | 37.5 | 37.5 | 12.5 | |||||||
| 4 | 6.25 | 25 | 37.5 | 25 | 6.25 | ||||||
| 5 | 3.13 | 15.63 | 31.25 | 31.25 | 15.63 | 3.13 | |||||
| 6 | 1.56 | 9.38 | 23.44 | 31.25 | 23.44 | 9.38 | 1.56 | ||||
| 7 | 0.78 | 5.47 | 16.41 | 27.34 | 27.34 | 16.41 | 5.47 | 0.78 | |||
| 8 | 0.39 | 3.13 | 10.94 | 21.88 | 27.34 | 21.88 | 10.94 | 3.13 | 0.39 | ||
| 9 | 0.2 | 1.76 | 7.03 | 16.41 | 24.61 | 24.61 | 16.41 | 7.03 | 1.76 | 0.2 | |
| 10 | 0.1 | 0.98 | 4.39 | 11.72 | 20.51 | 24.61 | 20.51 | 11.72 | 4.39 | 0.98 | 0.1 |
Formulas
| At most: | @@\mathrm{P}({\le}\,S\text{ successes on }N\text{ draws}) = \sum\limits_{i=0}^{S} \binom{i}{N}\,p^i\,(1 - p)^{N-i}@@ |
| Exact: | @@\mathrm{P}(\phantom{\le}\,S\text{ successes on }N\text{ draws}) = \binom{S}{N}\,p^S\,(1 - p)^{N-S}@@ |
| At least: | @@\mathrm{P}({\ge}\,S\text{ successes on }N\text{ draws}) = \sum\limits_{i=S}^{N} \binom{i}{N}\,p^i\,(1 - p)^{N-i}@@ |
Usage
- Click to one table element to set the corresponding @@N@@ and @@S@@ chart values.
- Press ESC key to reset to default values.
- 🔗 Link to this application with current values: http://www.opimedia.be/probability/success.html
Links
- The JavaScript file used by this application: success.js
- This application uses these other free softwares:
- Probability to win at least once