Probability Calculator
Calculate the probability of one or two independent events, including either/or and both together, with odds for and against.
Probability of event A
16.667%
0.16667 as a decimal · 1 in 6
Event B
50%
Odds against A
5 : 1
- P(A)
- 16.667% (0.16667)
- P(B)
- 50% (0.5)
- P(A and B) — independent
- 8.333%
- P(A or B) — either one
- 58.333%
- P(neither)
- 41.667%
- Odds in favour of A
- 0.2 : 1
- Odds against A
- 5 : 1
How this was calculated
- 1.P(A) = 1 ÷ 6 = 0.16667 = 16.667%.
- 2.P(B) = 1 ÷ 2 = 0.5 = 50%.
- 3.For independent events, P(A and B) = 0.1667 × 0.5 = 0.08333.
- 4.P(A or B) = P(A) + P(B) − P(A and B) = 0.58333.
The combined probabilities assume the events are independent — one outcome does not change the other, like two separate dice rolls.
How the probability calculation works
Probability is the number of ways something can happen divided by the number of possible outcomes. A single six on a fair die is 1 ÷ 6, or 16.67%.
For independent events, multiply to get the probability of both happening: two sixes is 1/6 × 1/6 = 1/36. Add to get either: 1/6 + 1/6, but subtract the overlap or you count it twice.
Odds are a different way of expressing the same thing: they compare favourable outcomes to unfavourable ones, rather than to the total.
Worked example
Rolling a six on a die (A) and flipping heads on a coin (B).
- →P(A) = 1/6 = 16.67%
- →P(B) = 1/2 = 50%
- →P(both) = 1/12 = 8.33%
Answer: 16.67% for a six, 50% for heads, and 8.33% for both together.
Probability FAQs
What does independent mean?
One event's outcome does not affect the other — separate coin flips, for example. Drawing cards without replacing them is dependent, and the multiplication rule changes.
Why subtract the overlap for either/or?
Because adding P(A) and P(B) counts the case where both happen twice. Subtracting P(A and B) once corrects the double count.
Can probability be above 100%?
No. A probability is always between 0 and 1, or 0% and 100%. If your calculation exceeds that, the events are not independent or the outcomes are miscounted.
Probability Calculator is part of the math calculators collection on Calcora, alongside 7 other tools. Results are calculated in your browser and are for information only — see our disclaimer.
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