Probability Calculator

Probability is evaluated from Favorable Outcomes, Total Possible Outcomes and P. The calculation reports Probability P, Complement P = 1 - P and Odds For.

Results

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About the Probability Calculator

Probability is treated here as a quantitative relation between Favorable Outcomes, Total Possible Outcomes and P and Probability P, Complement P = 1 - P, Odds For and P - Independent.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
P(A) = favorable / total
P(A′) = 1 - P(A)
P(A and B) = P(A) x P(B) [independent]
P(A or B) = P(A) + P(B) [mutually exclusive]

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

P(A) = favorable / total
P(A′) = 1 - P(A)
P(A and B) = P(A) x P(B) [independent]
P(A or B) = P(A) + P(B) [mutually exclusive]

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Drawing a Red Card from a Deck

Inputs

favorable: 26 total: 52 p_b: 0.5
Probability P: 0.5. Complement P = 1 - P: 0.5. Odds For: 26:26. P - Independent: 0.25. P - Mutually Excl.: 0.75

With Favorable Outcomes = 26, Total Possible Outcomes = 52 and P = 0.5 as the stated inputs, the result is Probability P = 0.5, Complement P = 1 - P = 0.5 and Odds For = 26:26. Each value corresponds to the declared output fields.

Example 2: Lottery Ticket — Complement Strategy

Inputs

favorable: 1 total: 14000000
Probability P: 0. Complement P = 1 - P: 1. Odds For: 1:13999999. P - Independent: 0. P - Mutually Excl.: 0

With Favorable Outcomes = 1 and Total Possible Outcomes = 14,000,000 as the stated inputs, the result is Probability P = 0, Complement P = 1 - P = 1 and Odds For = 1:13999999. Each value corresponds to the declared output fields.

Example 3: Rolling a Die — Multiple Events

Inputs

favorable: 2 total: 6 p_b: 0.1667
Probability P: 0.333333. Complement P = 1 - P: 0.666667. Odds For: 2:4. P - Independent: 0.055567. P - Mutually Excl.: 0.444467

With Favorable Outcomes = 2, Total Possible Outcomes = 6 and P = 0.1667 as the stated inputs, the result is Probability P = 0.333333, Complement P = 1 - P = 0.666667 and Odds For = 2:4. Each value corresponds to the declared output fields.

Example 4: Basketball Free Throws

Inputs

favorable: 8 total: 10 p_b: 0.8
Probability P: 0.8. Complement P = 1 - P: 0.2. Odds For: 8:2. P - Independent: 0.64. P - Mutually Excl.: 0.96

With Favorable Outcomes = 8, Total Possible Outcomes = 10 and P = 0.8 as the stated inputs, the result is Probability P = 0.8, Complement P = 1 - P = 0.2 and Odds For = 8:2. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate probability of rolling a die value
  • Find odds of winning a raffle
  • Combine probabilities of independent events
  • Convert probability to odds and back