What probability does decimal 2.5 imply?

The preset divides 1 by 2.5 and shows 2/5 = 40%. That is odds in favor of 2:3, odds against of 3:2, fractional odds of 3/2 and American odds of +150.

How do I enter fractional or American odds?

Choose Fractional odds and enter a profit/stake fraction such as 3/1, or choose American odds and enter a whole value such as +300 or -150. Fractional 3/1 and American +300 imply 25%; -150 implies 60%.

Are odds in favor and odds against interchangeable?

They reverse the ratio. Odds in favor of 1:3 mean favorable:unfavorable, so p = 1/4. Odds against of 3:1 mean unfavorable:favorable and give the same 1/4. Pick the matching format before entering the counts.

Does implied probability give the true chance?

It gives the arithmetic equivalent of the stated odds. It does not model a real event, remove a quoted margin or recommend a decision. All conversions preserve exact fractions internally; rounded decimal displays carry the approximate sign.

Will opening this preset change my main calculator settings?

No. This page has its own remembered draft. It opens at decimal odds of 2.5 on the first visit and remembers only edits made here; the main two-event draft stays separate.

Odds to Probability Calculator

Choose an odds format and enter its value. The converter gives the exact probability, percent, odds in favor and against, and equivalent decimal, fractional and American odds.

Odds and implied probability

Convert stated odds or a probability. Implied probability is arithmetic on the quoted price; it predicts no outcome and does not remove a margin.

Input format

Decimal odds

Enter total return per unit stake, such as 2.5.

Probability: 2/5 = 40%
Odds in favor: 2:3
Odds against: 3:2
Decimal odds: 2.5
Fractional odds: 3/2
American odds: +150

eventsA and B

P(A)

P(B)

Type each probability as a decimal (0.25), a percentage (25%) or a fraction (1/4).

How A and B relate

Type the probability that A and B both happen.

P(A and B)

Independent tries

Event repeated

Each try repeats the whole experiment, independently of the others, with the same probabilities.

Feasible P(A and B) for these entries

from max(0, 0.5 + 0.4 - 1) = 0 to min(0.5, 0.4) = 0.4

Venn diagram

Circles A and B overlap. A only 0.3, A and B 0.2, B only 0.2, outside both 0.3, total 1. The circles and their overlap are drawn to scale with each other; the box around them stands for everything else and is not to scale.

resultsfrom your entries, ≈ marks rounding

P(A and B): 0.2, entered
P(A or B): 0.5 + 0.4 - 0.2 = 0.7
P(not A): 1 - 0.5 = 0.5
P(not B): 1 - 0.4 = 0.6
P(A given B): 0.2 / 0.4 = 0.5
P(B given A): 0.2 / 0.5 = 0.4
A only: 0.5 - 0.2 = 0.3
B only: 0.4 - 0.2 = 0.2
Neither: 1 - 0.7 = 0.3
Exactly one: 0.7 - 0.2 = 0.5
P(A given not B): 0.3 / 0.6 = 0.5
P(B given not A): 0.2 / 0.5 = 0.4

A at least once in 2 tries: 1 - (1 - 0.5)^2 = 1 - 0.25 = 0.75
A in all 2 tries: (0.5)^2 = 0.25
A in none of the 2 tries: (1 - 0.5)^2 = 0.25

With these entries A and B are independent: P(A and B) = 0.2 equals P(A) x P(B) = 0.5 x 0.4 = 0.2.

Binomial, normal and Poisson questions have their own calculators: binomial, normal and Poisson.

Show as

P(A and B)

0.2

P(A or B)

0.7

P(A given B)

0.5

Neither

0.3

P(A) 0.5, P(B) 0.4independent, selected
P(A and B) = 0.5 x 0.4 = 0.2; P(A or B) = 0.5 + 0.4 - 0.2 = 0.7
P(A and B) entered as 0.45P(A) 0.5, P(B) 0.4
rejected: P(A and B) = 0.45 cannot be larger than P(B) = 0.4, because A and B together cannot happen more often than B alone. For these entries P(A and B) runs from 0 to 0.4.
At least one success in 2 triesindependent, p = 0.5 each
1 - (1 - 0.5)^2 = 1 - 0.25 = 0.75

Multiple independent events

Event probabilities

Enter 2 to 100 probabilities as decimals, percentages or fractions, separated by commas, semicolons or new lines. These can be different events; they need not have the same probability.

These events are independent

Confirm that these events are independent to combine their probabilities. Marginal probabilities alone cannot determine dependent events.

Combinations and probability

Count unordered selections with n choose k, then enter how many combinations meet your event. Probability is favorable combinations divided by all combinations, when every combination is equally likely. This does not count repeated selections or ordered arrangements.

Available items n

Items selected k

Favorable combinations

Each combination is equally likely

Confirm that each combination is equally likely before calculating the probability.

Accuracy. Every figure is exact fraction arithmetic on your entries, and a result that needs rounding for display is shown to six significant figures and marked ≈; a repeat count too long for exact fractions is worked in floating point and marked ≈ the same way. The page describes your assumptions and predicts nothing about real events: A and B are treated as independent only when you select it, and entries that cannot all hold together are refused with the range that would work. Binomial, normal and Poisson questions belong to the distribution calculators linked under the results.

Common questions

What probability does decimal 2.5 imply?: The preset divides 1 by 2.5 and shows 2/5 = 40%. That is odds in favor of 2:3, odds against of 3:2, fractional odds of 3/2 and American odds of +150.
How do I enter fractional or American odds?: Choose Fractional odds and enter a profit/stake fraction such as 3/1, or choose American odds and enter a whole value such as +300 or -150. Fractional 3/1 and American +300 imply 25%; -150 implies 60%.
Are odds in favor and odds against interchangeable?: They reverse the ratio. Odds in favor of 1:3 mean favorable:unfavorable, so p = 1/4. Odds against of 3:1 mean unfavorable:favorable and give the same 1/4. Pick the matching format before entering the counts.
Does implied probability give the true chance?: It gives the arithmetic equivalent of the stated odds. It does not model a real event, remove a quoted margin or recommend a decision. All conversions preserve exact fractions internally; rounded decimal displays carry the approximate sign.
Will opening this preset change my main calculator settings?: No. This page has its own remembered draft. It opens at decimal odds of 2.5 on the first visit and remembers only edits made here; the main two-event draft stays separate.

Every figure is exact fraction arithmetic on your entries, and a result that needs rounding for display is shown to six significant figures and marked ≈; a repeat count too long for exact fractions is worked in floating point and marked ≈ the same way. The page describes your assumptions and predicts nothing about real events: A and B are treated as independent only when you select it, and entries that cannot all hold together are refused with the range that would work. Binomial, normal and Poisson questions belong to the distribution calculators linked under the results.