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Probability of Compound Events

  • Grade 7
  • Mathematics
  • 7.SP.C.8
  • Statistics & Probability
  • Free lesson

Aligned to 7.SP.C.8 — Common Core State Standards for Mathematics.

What this lesson teaches

A compound event involves two or more simple events. Count all equally likely outcomes using an organized list, table, or tree diagram, then form the fraction (favorable outcomes) ÷ (total outcomes).

Worked examples

Example 1

Flip a coin and roll a die. There are 2 × 6 = 12 equally likely outcomes. P(heads and a 3) = 1/12, since only the one outcome (H, 3) works.

Example 2

Draw two marbles from a bag of 3 red and 2 blue, without replacing the first. P(both red) = (3/5) × (2/4) = 6/20 = 3/10.

Example 3

With replacement the second draw is unchanged: (3/5) × (3/5) = 9/25. Whether you put the first one back changes the answer.

Practice questions

  1. Two coins are flipped. List the outcomes and find P(two heads).
  2. A die is rolled twice. How many total outcomes are there?
  3. Spin a spinner with 3 equal colors and flip a coin. Find P(red and heads).

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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En español

Probabilidad de Eventos Compuestos

Un evento compuesto incluye dos o más eventos simples. Cuenta todos los resultados igualmente probables con una lista organizada, una tabla o un diagrama de árbol, y luego forma la fracción (resultados favorables) ÷ (resultados totales).

Ejemplo 1: Lanza una moneda y un dado. Hay 2 × 6 = 12 resultados igualmente probables. P(cara y un 3) = 1/12, porque solo funciona el único resultado (cara, 3).

Ejemplo 2: Saca dos canicas de una bolsa con 3 rojas y 2 azules, sin devolver la primera. P(las dos rojas) = (3/5) × (2/4) = 6/20 = 3/10.

Ejemplo 3: Con devolución, el segundo sorteo no cambia: (3/5) × (3/5) = 9/25. Si devuelves o no la primera, cambia la respuesta.

More Statistics & Probability lessons

Sampling, Comparing Data, and Probability7.SP.C.5Random Samples & Representative Data7.SP.A.1Drawing Inferences from Samples7.SP.A.2Comparing Data with Visual Overlap7.SP.B.3Comparing Populations with Center & Spread7.SP.B.4Estimating Probability from Data7.SP.C.6

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