worldofcalcsProbability Calculator
Probability of an event
Probability
1/13
0.0769 · 7.69%
Doesn't happen
12/13
0.9231 · 92.31%
Odds in favour
1 : 12
Two independent events
As a fraction, decimal or %, e.g. 1/6, 0.5 or 50%
Both A and B
8.33%
0.0833
A or B (at least one)
58.33%
0.5833
Exactly one
50%
0.5
Neither
41.67%
0.4167
Repeated tries
At least once
51.77%
0.5177
Every time
0.08%
0.0008
Never
48.23%
0.4823
What is probability?
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). When all outcomes are equally likely, it's the number of favourable outcomes divided by the total number of outcomes. This calculator gives the answer as a fraction, decimal and percentage, combines two independent events, and finds the chance of something happening at least once in several tries.
Probability formulas
P(E) = favourable ÷ total · P(not E) = 1 − P(E) · P(A and B) = P(A) × P(B) · P(A or B) = P(A) + P(B) − P(A) × P(B) · P(at least once in n) = 1 − (1 − p)ⁿ
The 'and' and 'or' rules here assume the events are independent, meaning one doesn't affect the other, like a coin toss and a dice roll. For events that can't happen together, P(A or B) = P(A) + P(B).
Common mistakes
- Probabilities are never below 0 or above 1. If you get 1.2, something has been counted twice.
- Past results don't change independent events: after five heads in a row, the next toss is still 1/2.
- 'At least once' is easiest through the complement: 1 − P(never). The chance of at least one six in 4 rolls is 1 − (5/6)⁴ ≈ 51.77%.
- Odds and probability differ: a probability of 1/4 means odds of 1 : 3 (one favourable to three unfavourable).
- Two dice have 36 equally likely outcomes, not 11 totals. A sum of 7 has 6 ways and is the most likely total.
Worked example: drawing a king
- A card is drawn from a well-shuffled deck of 52 cards
- There are 4 kings, so 4 favourable outcomes out of 52
- P(king) = 4/52 = 1/13 ≈ 0.0769, or 7.69%
- P(not a king) = 1 − 1/13 = 12/13, or 92.31%
- Odds in favour of a king: 1 : 12
Probabilities of common events
Coin, dice and card questions from school textbooks.
| Event | Favourable / total | Probability | Percentage |
|---|---|---|---|
| Heads on a coin | 1/2 | 1/2 | 50% |
| A 6 on a dice | 1/6 | 1/6 | 16.67% |
| An even number on a dice | 3/6 | 1/2 | 50% |
| A king from a deck | 4/52 | 1/13 | 7.69% |
| A heart from a deck | 13/52 | 1/4 | 25% |
| A red face card | 6/52 | 3/26 | 11.54% |
| A sum of 7 with two dice | 6/36 | 1/6 | 16.67% |
| Two heads with two coins | 1/4 | 1/4 | 25% |
A standard deck has 52 cards: 4 suits of 13, with 12 face cards (jack, queen and king).