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 | 96 | 4 | |||||||||
| 2 | 92.16 | 7.68 | 0.16 | ||||||||
| 3 | 88.47 | 11.06 | 0.46 | 0.01 | |||||||
| 4 | 84.93 | 14.16 | 0.88 | 0.02 | ~0 | ||||||
| 5 | 81.54 | 16.99 | 1.42 | 0.06 | ~0 | ~0 | |||||
| 6 | 78.28 | 19.57 | 2.04 | 0.11 | ~0 | ~0 | ~0 | ||||
| 7 | 75.14 | 21.92 | 2.74 | 0.19 | 0.01 | ~0 | ~0 | ~0 | |||
| 8 | 72.14 | 24.05 | 3.51 | 0.29 | 0.02 | ~0 | ~0 | ~0 | ~0 | ||
| 9 | 69.25 | 25.97 | 4.33 | 0.42 | 0.03 | ~0 | ~0 | ~0 | ~0 | ~0 | |
| 10 | 66.48 | 27.7 | 5.19 | 0.58 | 0.04 | ~0 | ~0 | ~0 | ~0 | ~0 | ~0 |
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?p=4
Links
- The JavaScript file used by this application: success.js
- This application uses these other free softwares:
- Probability to win at least once