Basic Probability Calculator

Basic Probability is evaluated from Favorable Outcomes, Total Possible Outcomes and Favorable Outcomes. The calculation reports P, P as% and P Complement.

Results

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About the Basic Probability Calculator

Basic Probability is treated here as a quantitative relation between Favorable Outcomes, Total Possible Outcomes and Favorable Outcomes and P, P as%, P Complement and P.

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:
Divide favorable outcomes by total outcomes. Complement = 1 minus probability. For two independent events: multiply probabilities for AND, use inclusion-exclusion for OR.

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:

Divide favorable outcomes by total outcomes. Complement = 1 minus probability. For two independent events: multiply probabilities for AND, use inclusion-exclusion for OR.

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: Rolling a standard die: P(rolling a 4)

Inputs

favorable_a: 1 total: 6
P: 0.1667. P as%: 16.67%. P Complement: 0.8333. P: 0.3333. P Both independent: 0.4444. P Both independent: 0.0556

With Favorable Outcomes = 1 and Total Possible Outcomes = 6 as the stated inputs, the result is P = 0.1667, P as% = 16.67% and P Complement = 0.8333. Each value corresponds to the declared output fields.

Example 2: Drawing cards: P(drawing an Ace from 52-card deck)

Inputs

favorable_a: 4 total: 52
P: 0.0769. P as%: 7.69%. P Complement: 0.9231. P: 0.0385. P Both independent: 0.1124. P Both independent: 0.003

With Favorable Outcomes = 4 and Total Possible Outcomes = 52 as the stated inputs, the result is P = 0.0769, P as% = 7.69% and P Complement = 0.9231. Each value corresponds to the declared output fields.

Example 3: Defective products: 12 defective out of 200. P(random item is defective)

Inputs

favorable_a: 12 total: 200
P: 0.06. P as%: 6%. P Complement: 0.94. P: 0.01. P Both independent: 0.0694. P Both independent: 0.0006

With Favorable Outcomes = 12 and Total Possible Outcomes = 200 as the stated inputs, the result is P = 0.06, P as% = 6% and P Complement = 0.94. Each value corresponds to the declared output fields.

Example 4: Coin flip then die roll: P(heads) and P(rolling 6) — what's P(both)?

Inputs

favorable_a: 1 total: 2 favorable_b: 1
P: 0.5. P as%: 50%. P Complement: 0.5. P: 0.5. P Both independent: 0.75. P Both independent: 0.25

With Favorable Outcomes = 1, Total Possible Outcomes = 2 and Favorable Outcomes = 1 as the stated inputs, the result is P = 0.5, P as% = 50% and P Complement = 0.5. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate probability of a single event
  • Find complement probability
  • Calculate probability of two independent events