Math Tools
Calculate single event or independent two-event probabilities.
Probability
16.7%
0.1667 as a decimal
Probability is the likelihood of an event occurring, calculated as favorable outcomes divided by total outcomes. Odds express the ratio of favorable to unfavorable outcomes.
Probability is the mathematical measure of how likely an event is to happen, ranging from 0 (impossible) to 1 (certain). A probability calculator automates the computation of theoretical probabilities for single events, combined events (AND/OR), and conditional scenarios. It eliminates manual fraction arithmetic and reduces errors when working with odds.
The calculator uses the fundamental probability formula: divide the number of favorable outcomes by the total number of possible outcomes. For multiple independent events, it multiplies individual probabilities (AND scenarios) or adds them and subtracts overlap (OR scenarios). For dependent events, it applies conditional probability by updating the denominator after each draw or selection, mimicking real drawing-without-replacement situations.
P(A) = Favorable Outcomes / Total Possible Outcomes. Combined: P(A AND B) = P(A) × P(B); P(A OR B) = P(A) + P(B) − P(A AND B)P(A) is the probability of event A; favorable outcomes are results you want to count; total outcomes include all possibilities. For combined events, multiply independent probabilities or add them and subtract overlap to avoid double-counting.
| Input | Result | Notes |
|---|---|---|
| Rolling a 4 on a standard six-sided die | 0.1667 or 16.67% or 1 in 6 | One favorable outcome (rolling 4) out of six total (1–6) |
| Drawing a red card from a shuffled standard deck (52 cards, 26 red) | 0.50 or 50% or 1 in 2 | 26 favorable (red cards) ÷ 52 total = 0.5; this is independent of previous draws if replaced |
| Flipping heads AND rolling a 3: both independent | 0.0833 or 8.33% or 1 in 12 | 0.5 (heads) × 0.1667 (rolling 3) = 0.0833; multiply independent probabilities |
Probability is favorable outcomes ÷ total outcomes (ranges 0–1). Odds express the ratio of favorable to unfavorable outcomes, often written '1 in 6' or '1:5'. A probability of 0.167 (1 in 6) corresponds to odds of 1:5 (one win for every five losses).
Count favorable outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 ways. Total outcomes = 6 × 6 = 36. Probability = 6 ÷ 36 = 0.1667 or 16.67%.
Conditional probability is the likelihood of event B given that event A has already occurred. Example: probability of drawing a second red card, given you already drew one red card from the deck (denominator drops to 51, favorable count to 25).
No. A probability of 1 means the event is certain; a probability of 0 means it is impossible. Any value above 1 or below 0 indicates a calculation error. The sum of all mutually exclusive outcomes in a sample space must equal 1.
Use P(at least one) = 1 − P(none). Example: probability of rolling at least one 6 in three die rolls = 1 − (5/6)³ = 1 − 0.5787 = 0.4213 or 42.13%.
As you repeat an experiment many times, the observed frequency of an outcome approaches its theoretical probability. Rolling a die 6 times may show three 5s, but rolling 6,000 times yields roughly 1,000 fives (≈16.67%), proving the theory.