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Develop Non-Uniform Probability Models

Students develop probability models for non-uniform situations—where outcomes are not equally likely—using observed frequencies or context clues. They assign probabilities that are consistent (sum to 1) and use models to find probabilities of events and to detect unfairness in experiments.

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Develop Non-Uniform Probability Models

Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

0.1 + 0.4 + = 1

How it is taught

0:00 of 4:37

In a non-uniform model, outcomes are not equally likely.

Each outcome still gets a probability.

All those probabilities must sum to 1.

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.

70 hits in 80 trials: P = ___ — 0.875. P is the event's part of all 80: 70 ÷ 80 = 0.875.

Bag of marbles · 5 red, 3 blue, 2 green

Imagine a bag with ten marbles — five red, three blue, and two green. The colors aren't balanced, so the probabilities won't be either.

Let's build a probability model. What's the chance of pulling each color?

Five of the ten marbles are red, so the probability of red is five tenths.

Three are blue, so the probability of blue is three tenths.

Two are green, so the probability of green is two tenths.

Now check the model. Five tenths plus three tenths plus two tenths equals ten tenths — that's one whole. The probabilities are consistent!

10 marbles · 5 red, 3 blue, 2 greenOutcomes aren't equally likely → non-uniform modelBuild the probability modelRedBlueGreenP(red) =510P(blue) =310P(green) =210510 + 310 + 210 = 1010 = 1All probabilities sum to 1 — the model is consistent.What is P(not red)?P(not red) = P(blue) + P(green)= 310 + 210= 510 = 12Non-uniform: outcomes aren't equal, but probabilities still sum to 1.P(NOT RED)12= 510
Grade 7 · When outcomes aren't equally likely

Now use the model. What's the chance the marble is NOT red? Add the blue and green probabilities: three tenths plus two tenths is five tenths, or one half.

That's a non-uniform probability model. The outcomes aren't equally likely — but the probabilities still add up to one.

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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