Calculate P(E), complement, odds ratio and log-odds from any event count and sample space. Shows fraction, decimal, and binomial trial stats instantly.
Most probability questions reduce to the same arithmetic: how many outcomes you care about, divided by how many outcomes are possible. Probability Calculator makes that step immediate. Enter a favourable outcome count and a sample space size and it returns P(E) as both a decimal and a reduced fraction, the complement P(E′), the odds ratio, and the log-odds in one panel. The lead sample is rolling a 3 on a standard six-sided die: 1 favourable outcome out of 6, giving P(E) = 1/6 ≈ 0.166667, complement 5/6 ≈ 0.833333, odds 1 : 5, log-odds ≈ −1.6094.
Probability shows up in card games (13 hearts out of 52 = exactly 0.25), manufacturing quality control (3 defects in a batch of 200 = 0.015), and any scenario where you need to know how likely a single trial is before deciding whether to run a thousand of them.
Log-odds is ln(p / (1 − p)). It is the quantity logistic regression models work in, useful for comparing two events on the same scale: a log-odds of 0 means exactly 50/50; negative values mean the event is less likely than not; positive values mean more likely than not. For rolling a 3 (p ≈ 0.167) the log-odds is ≈ −1.6094. For drawing a heart from a deck (p = 0.25) it is ≈ −1.0986. For the true/false test sample (p = 0.75) it is ≈ +1.0986, the mirror image, as expected. When p = 0 or p = 1 the log-odds is ±∞ and the tool reports that explicitly rather than showing a number that would silently overflow.
The binomial trial stats treat the sample space size as n and use E[X] = n × p, Var = n × p × (1 − p), Std Dev = √Var.
P(E)
0.166667
1/6
P(E′)
0.833333
5/6
Odds
1 : 5
for : against
Log-odds
-1.6094
ln(p / 1−p)
Binomial Trial Stats — treating sample space as n
E[X] = n·p
1
Var = n·p·q
0.8333
Std Dev
0.9129