Manuals/calci/BINOMIALPROBABILITY

BINOMIALPROBABILTY(NumberOftrials,NumberOfSuccess,ProbabiltyOfSuccess)

• $==Description==*ThisfunctiongivestheprobabilityvalueoftheBinomialdistribution.*Abinomialexperimenthasthefollowingcharacteristics:*1.Theexperimentinvolvesrepeatedtrials.*2.Eachtrialhasonlytwopossibleoutcomes-asuccessorafailure.*3.Theprobabilitythataparticularoutcomewilloccuronanygiventrialisconstant.*4.Allofthetrialsintheexperimentareindependent.*AbinomialprobabilityreferstotheprobabilityofgettingEXACTLYrsuccessesinaspecificnumberoftrials.*Thenumberoftrialsreferstothenumberofattemptsinabinomialexperiment.*Thenumberoftrialsisequaltothenumberofsuccessesplusthenumberoffailures.*Whencomputingabinomialprobability,itisnecessarytocalculateandmultiplythreeseparatefactors:*1.thenumberofwaystoselectexactlyrsuccesses,*2.theprobabilityofsuccess(p)raisedtotherpower,*3.theprobabilityoffailure(q)raisedtothe(n-r)power.*TheformulaforBinomialprobabilityis:<math>{\binom {n}{r}}p^{r}.q^{n-r}$ or ${\binom {n}{r}}p^{r}(1-p)^{n-r}$

where n = number of trials,r = number of specific events you wish to obtain.
p = probability that the event will occur, q = probability that the event will not occur.(q = 1 - p, the complement of the event)

Examples

1. BINOMIALPROBABILTY(5,3,0.4)=0.23040000000000005
2. BINOMIALPROBABILTY(10,4,0.25)=0.1459980010986328
3. BINOMIALPROBABILTY(12,11,0.75)=0.12670540809631348

See Also

• LEVENESTEST
• MOODSMEDIANTEST
• RIEMANNZETA

References

• Binomial probability