The Addition Rule for Probability
Aligned to S-CP.B.7 — Common Core State Standards for Mathematics.
What this lesson teaches
The Addition Rule states P(A or B) = P(A) + P(B) − P(A and B). Subtracting the overlap keeps outcomes shared by both events from being counted twice.
Worked examples
Example 1
Draw one card from a deck. P(king) = 4/52, P(heart) = 13/52, and P(king of hearts) = 1/52. So P(king or heart) = 4/52 + 13/52 − 1/52 = 16/52 = 4/13.
Example 2
Roll two dice. P(sum is 7) = 6/36 and P(at least one die shows a 4) = 11/36. The overlap — a sum of 7 containing a 4 — is the two rolls (3,4) and (4,3), so 2/36. Then P(sum is 7 or a 4 appears) = 6/36 + 11/36 − 2/36 = 15/36 = 5/12.
Example 3
Common mistake: forgetting to subtract the overlap. Adding 4/52 + 13/52 gives 17/52, counting the king of hearts twice — once as a king and once as a heart. The subtraction is needed whenever the two events CAN both happen. If they are mutually exclusive, the overlap is 0 and the rule simplifies to plain addition, but check that before skipping the step.
Practice questions
- State the Addition Rule for P(A or B).
- If P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.1, find P(A or B).
- On a die roll, find P(even or greater than 4).
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
La Regla de la Suma en probabilidad
La Regla de la Suma establece P(A o B) = P(A) + P(B) − P(A y B). Restar la intersección evita que los resultados compartidos por ambos eventos se cuenten dos veces.
Ejemplo 1: Saca una carta de una baraja. P(rey) = 4/52, P(corazón) = 13/52 y P(rey de corazones) = 1/52. Así, P(rey o corazón) = 4/52 + 13/52 − 1/52 = 16/52 = 4/13.
Ejemplo 2: Lanza dos dados. P(la suma es 7) = 6/36 y P(al menos un dado muestra un 4) = 11/36. El traslape — una suma de 7 que contenga un 4 — son los lanzamientos (3,4) y (4,3), o sea 2/36. Entonces P(la suma es 7 o aparece un 4) = 6/36 + 11/36 − 2/36 = 15/36 = 5/12.
Ejemplo 3: Error común: olvidar restar el traslape. Sumar 4/52 + 13/52 da 17/52 y cuenta dos veces el rey de corazones — una como rey y otra como corazón. La resta hace falta siempre que los dos eventos PUEDAN ocurrir juntos. Si son mutuamente excluyentes, el traslape es 0 y la regla se reduce a una suma simple, pero compruébalo antes de saltarte el paso.
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