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Approximate Probability from Experimental Data

Students collect data from chance processes (experiments, simulations) and use the relative frequency of outcomes to approximate probability. They compare experimental probability to theoretical probability and understand that more trials produce more reliable approximations.

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Approximate Probability from Experimental Data

Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

Simon spun a prize wheel 10 times, and it stopped on the grand prize 1 time. What is the experimental probability of the grand prize, as a decimal?

How it is taught

0:00 of 4:21

Experimental probability is how often an event happened in trials.

It is the count of hits divided by the total tries.

That result can be scaled to a new number of tries.

Read it: Probability from 0 to 1

13 of 20 equally likely outcomes are the event. P is the event's part of all of them: 13 ÷ 20 = 0.65, more than 1/2, so the event is likely.

  1. Count the outcomes in the event, and all the outcomes.
  2. Divide the event's count by the count of all of them.
  3. Place P on the line: near 0 is unlikely, near 1 is likely.

P is a part of the whole, so it runs from 0, impossible, to 1, certain.

All the chances in a model add to 1. Not the event is all the rest: 7 of 20, so P(not) = 0.35, and 0.65 + 0.35 = 1.

A count comes back from P too: 0.65 of the 20 outcomes is 13 of them.

P = the event's outcomes ÷ all the outcomes, a number from 0 to 1.

Dividing by the outcomes that are not the event: 13 ÷ 7, the odds.

P divides by all 20 outcomes: 13 ÷ 20 = 0.65.

56 hits in 80 trials: P = ___ — 0.7. P is the event's part of all 80: 56 ÷ 80 = 0.7.

Rolled a die 60 times, got '4' twelve times

Sometimes we don't know a probability — we have to find it from data. Let's see how!

We rolled a die sixty times and recorded the results. A four came up twelve times.

Experimental probability equals the number of times the event happened, divided by the total trials.

Plug in our numbers: twelve fours out of sixty rolls.

Simplify by dividing the top and bottom by twelve. That gives us one fifth.

One in every five rolls landed on a four — here's what that looks like.

The theoretical probability is one out of six, since a fair die has six equal faces.

One fifth is zero point two. One sixth is about zero point one-seven. Close, but not equal.

If we rolled hundreds more times, our experimental probability would creep closer to one sixth.

From our data, the experimental probability of rolling a four is about one fifth.

What's the chance of rolling a 4?Let's find out — with real data!Our experimentTotal rolls:60Got a 4:12Experimental probability:times event happenedtotal trials1260← fours← rolls1260÷12÷12=151 out of every 5 rollsP(4) ≈ 15 = 0.20Theoretical probability1 favorable face out of 6 total faces16≈ 0.17How close are they?00.31615theoretical ≈ 0.17experimental = 0.20More trials → closer to theoreticalRoll 600 times — even closer. Roll 6,000 — closer still.P(rolling a 4)15≈ 0.20 from 60 trialsExperimental:1260=15= 0.20 = 20%
Grade 7 · Using data to estimate probability

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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