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Estimating Probability from Data

  • Grade 7
  • Mathematics
  • 7.SP.C.6
  • Statistics & Probability
  • Free lesson

Aligned to 7.SP.C.6 — Common Core State Standards for Mathematics.

What this lesson teaches

The experimental probability of an event is the fraction of times it happens: (number of times it occurs) ÷ (total trials). As the number of trials grows, this long-run relative frequency gets close to the true probability.

Worked examples

Example 1

A spinner lands on red 18 times in 60 spins. Experimental probability of red = 18 ÷ 60 = 0.3, or 30%.

Example 2

A thumbtack lands point-up 42 times in 200 drops. Experimental probability = 42 ÷ 200 = 0.21.

Example 3

Experimental probability gets closer to theoretical as trials increase. Ten coin flips might give 7 heads; ten thousand will sit very near half.

Practice questions

  1. A coin lands heads 27 times in 50 flips. Find the experimental probability of heads.
  2. A bag draw gives blue 45 times in 150 tries. Estimate P(blue) as a fraction and a percent.
  3. Why does flipping a coin 500 times estimate P(heads) better than flipping it only 10 times?

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

Estimar la Probabilidad a partir de Datos

La probabilidad experimental de un evento es la fracción de veces que ocurre: (número de veces que ocurre) ÷ (total de intentos). Al aumentar los intentos, esta frecuencia relativa a largo plazo se acerca a la probabilidad verdadera.

Ejemplo 1: Una ruleta cae en rojo 18 veces en 60 giros. Probabilidad experimental de rojo = 18 ÷ 60 = 0.3, o sea 30%.

Ejemplo 2: Una tachuela cae con la punta hacia arriba 42 veces en 200 lanzamientos. Probabilidad experimental = 42 ÷ 200 = 0.21.

Ejemplo 3: La probabilidad experimental se acerca a la teórica al aumentar los intentos. Diez lanzamientos de moneda pueden dar 7 caras; diez mil quedarán muy cerca de la mitad.

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.4Building a Probability Model7.SP.C.7

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