← Back 007 · CALCULATORS / PROBABILITY

Probability
Calculator.

Modify the values in any of the four calculators below and the results update live. Find the union, intersection and complement of two independent events, solve for the missing probabilities from any two, compute repeated trials, or measure the area under a normal distribution between two bounds.

// Probability of Two Events Assumes A and B are independent

Probability of A: P(A) Values between 0 and 1. Probability of B: P(B) Values between 0 and 1.

P(A')—

P(B')—

P(A ∩ B)—

P(A ∪ B)—

P(A Δ B)—

P((A ∪ B)')—

// Probability Solver for Two Events Fill any 2 — the rest are derived

P(A) P(B) P(A') P(B') P(A ∩ B) P(A ∪ B) P(A Δ B) P((A ∪ B)')

Values must be between 0 and 1. Highlighted fields are computed.

// Probability of a Series of Independent Events

Event A — Probability Event A — Repeat Times Event B — Probability Event B — Repeat Times

P(A all n times)—

P(A never)—

P(A at least once)—

P(B all m times)—

P(B never)—

P(B at least once)—

P(A all AND B all)—

P(A ≥1 AND B ≥1)—

// Probability of a Normal Distribution P(Lb ≤ X ≤ Rb)

Mean (µ) Standard Deviation (σ) Left Bound (Lb) Use -inf for negative infinity. Right Bound (Rb) Use inf for positive infinity.

// Area P

—

Enter μ, σ and the two bounds.

50% CI—

80% CI—

90% CI—

95% CI—

99% CI—

99.9% CI—

// Related

Probability of two events

Probability is the measure of the likelihood of an event occurring, quantified as a number between 0 and 1, with 1 meaning certainty and 0 meaning impossibility. In its most general form, probability equals desired outcomes ÷ total outcomes. The formulas below assume two events A and B are independent.

Complement of A and B

P(A') = 1 − P(A)
P(B') = 1 − P(B)

Intersection · Union · XOR

P(A ∩ B) = P(A) × P(B)                ; independent
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A Δ B) = P(A) + P(B) − 2·P(A ∩ B)
P((A ∪ B)') = 1 − P(A ∪ B)

Series of independent events

If P(A) is the probability of event A in one trial and it is repeated n independent times:

P(A all n times)     = P(A)^n
P(A never)           = (1 − P(A))^n
P(A at least once)   = 1 − (1 − P(A))^n

Normal distribution

For a normal distribution with mean μ and standard deviation σ, the probability that Lb ≤ X ≤ Rb is given by:

P(Lb ≤ X ≤ Rb) = Φ((Rb − μ) / σ) − Φ((Lb − μ) / σ)

// Z Table — area from mean (0 to Z)

ProbabilityCalculator.