Building a Probability Model
Aligned to 7.SP.C.7 — Common Core State Standards for Mathematics.
What this lesson teaches
A probability model lists the possible outcomes and each outcome's probability, and all probabilities add to 1. In a uniform model every outcome is equally likely; otherwise you use observed data.
Worked examples
Example 1
A fair number cube has outcomes 1–6, each with probability 1/6. P(a number greater than 4) = P(5) + P(6) = 1/6 + 1/6 = 2/6 = 1/3.
Example 2
A spinner has 4 equal sections: 2 blue, 1 red, 1 green. P(blue) = 2/4 = 1/2, P(not blue) = 1/2.
Example 3
All probabilities in a model must sum to 1. If P(red) = 0.3 and P(blue) = 0.5, then everything else together must be 0.2.
Practice questions
- A fair coin is flipped. List the model and give P(tails).
- A spinner has 4 equal sections: red, blue, green, yellow. Find P(not red).
- A fair die is rolled. Find P(an even number).
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.
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Construir un Modelo de Probabilidad
Un modelo de probabilidad lista los resultados posibles y la probabilidad de cada uno, y todas las probabilidades suman 1. En un modelo uniforme cada resultado es igualmente probable; si no, usas datos observados.
Ejemplo 1: Un dado justo tiene los resultados 1–6, cada uno con probabilidad 1/6. P(un número mayor que 4) = P(5) + P(6) = 1/6 + 1/6 = 2/6 = 1/3.
Ejemplo 2: Una ruleta tiene 4 secciones iguales: 2 azules, 1 roja, 1 verde. P(azul) = 2/4 = 1/2, P(no azul) = 1/2.
Ejemplo 3: Todas las probabilidades de un modelo deben sumar 1. Si P(rojo) = 0.3 y P(azul) = 0.5, todo lo demás junto debe ser 0.2.
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