Hypergeometric Probability Calculator
Odds of drawing a given number of the right things, when you draw without putting them back.
Results
Chance of exactly that many
6.697314
%
That is one chance in
15
Chance of that many or fewer
99.5221
%
Chance of that many or more
7.1752
%
How many you would get on average
0.5000
Is that even possible
Yes
Fewest you could possibly get
0
Most you could possibly get
5
What this tool does
This is the binomial's honest cousin. The binomial assumes every draw has the same chance — coins, dice, clicks. But when you deal cards, pull balls from a bag, or pick items off a line to inspect, each one you take changes what is left behind, and the binomial starts to lie. This is the maths behind lottery odds, acceptance sampling and every question shaped like "I drew 5 from 50, how many of the 7 good ones did I get?".
Formula
P(exactly k) = C(good, k) × C(rest, drawn − k) ÷ C(total, drawn)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
population | How many there are in total | — |
successes | How many of those are the kind you want | — |
draws | How many you take out | — |
hits | How many of the wanted kind you get | — |
PX | Chance of exactly that many | % |
OI | That is one chance in | — |
LE | Chance of that many or fewer | % |
GE | Chance of that many or more | % |
EX | How many you would get on average | — |
OK | Is that even possible | — |
KL | Fewest you could possibly get | — |
KH | Most you could possibly get | — |
Worked example
- How many there are in total50
- How many of those are the kind you want5
- How many you take out5
- How many of the wanted kind you get2
- Chance of exactly that many6.697314 %
- That is one chance in15
- Chance of that many or fewer99.5221 %
- Chance of that many or more7.1752 %
- How many you would get on average0.5000
- Is that even possibleYes
- Fewest you could possibly get0
- Most you could possibly get5
Limitations
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.