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How This Calculator Works
Probability measures how likely an event is, as a number between 0 (impossible) and 1
(certain). Enter a count of favorable and total outcomes to find a single event’s probability
and its complement, or enter two independent events’ probabilities to find the chance both happen,
either happens, or neither happens.
The Formula
Single event:
Probability=Total OutcomesFavorable Outcomes
The complement (the chance the event does NOT happen) is always 1−Probability.
Two independent events (where one event happening doesn’t change the chance of the other):
P(both occur)=P(A)×P(B)
P(either occurs)=P(A)+P(B)−P(A)×P(B) — adding the two
directly would double-count the overlap where both happen, so it’s subtracted back out once (the
inclusion-exclusion principle).
P(neither occurs)=(1−P(A))×(1−P(B))
Worked Example
Single event: rolling an even number on a standard 6-sided die.
Favorable outcomes: 3 (2, 4, 6) out of 6 total: 3÷6=50%.
Complement: 1−50%=50% (rolling an odd number).
Two independent events: flipping a coin and getting heads (P = 50%) AND rolling a die and
getting a 6 (P ≈ 16.67%):
P(both) = 0.5 × 0.1667 ≈ 8.33%
P(either) = 0.5 + 0.1667 − 0.0833 ≈ 58.33%
P(neither) = 0.5 × 0.8333 ≈ 41.67%
Cómo funciona esta calculadora
La probabilidad mide qué tan probable es un evento, como un número entre 0 (imposible) y 1
(seguro). Ingresa un número de resultados favorables y totales para encontrar la probabilidad de
un solo evento y su complemento, o ingresa las probabilidades de dos eventos independientes para
encontrar la posibilidad de que ambos ocurran, de que ocurra alguno de los dos, o de que no ocurra
ninguno.
El complemento (la posibilidad de que el evento NO ocurra) siempre es 1−Probabilidad.
Dos eventos independientes (donde que ocurra uno no cambia la probabilidad del otro):
P(ambos ocurren)=P(A)×P(B)
P(ocurre alguno)=P(A)+P(B)−P(A)×P(B) — sumar los dos
directamente contaría dos veces la superposición donde ambos ocurren, así que se resta una vez
(el principio de inclusión-exclusión).
P(no ocurre ninguno)=(1−P(A))×(1−P(B))
Ejemplo resuelto
Evento único: obtener un número par al lanzar un dado estándar de 6 caras.
Resultados favorables: 3 (2, 4, 6) de 6 totales: 3÷6=50%.
Complemento: 1−50%=50% (obtener un número impar).
Dos eventos independientes: lanzar una moneda y obtener cara (P = 50%) Y lanzar un dado y
obtener un 6 (P ≈ 16.67%):
Two events are independent if one happening has no effect on the chance of the other happening — like a coin flip and a separate die roll. If one event DOES affect the other (dependent events), these formulas do not apply.
Why do you subtract P(A) x P(B) when finding P(either occurs)?
Simply adding P(A) and P(B) would count the case where BOTH happen twice — once in each probability. Subtracting the overlap (P(A) x P(B)) back out corrects for that double-count. This is called the inclusion-exclusion principle.
What is a complement in probability?
An event's complement is everything that counts as the event NOT happening. Since an event either happens or it doesn't, an event's probability and its complement's probability always add up to exactly 1 (100%).
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