Develop Uniform Probability Models

Students develop and use uniform probability models—where all outcomes are equally likely—to find probabilities of events. They list all possible outcomes of a simple experiment, assign equal probabilities, and compute the probability of compound events by counting favorable outcomes.

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Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

2 of 5 equally likely outcomes: P(not) =

How it is taught

0:00 of 4:02

A uniform model makes every outcome equally likely.

Each outcome has the same probability.

An event's probability is favorable outcomes over all outcomes.

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.

Count the outcomes in the event, and all the outcomes.
Divide the event's count by the count of all of them.
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.

5 of 9 equally likely outcomes: P = ___ — 5/9. P is the event's part of all 9: 5/9.

P(even) on a fair die

When we roll a fair six-sided die, what's the chance of getting an even number?

First, let's list every possible outcome: one, two, three, four, five, and six.

Because the die is fair, each outcome is equally likely. That's called a uniform probability model.

So each outcome has the same probability: one out of six.

Our event is rolling an even number. Which outcomes are even?

Two, four, and six are even. Those are our favorable outcomes.

That gives us three favorable outcomes.

Out of six total outcomes in all.

Grade 7 · Equally likely outcomes

So the probability is favorable over total — three over six.

Three over six simplifies to one half.

The probability of rolling an even number is one half, or fifty percent. Nice work!

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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Standards

CCSS.7.SP.C.7

Develop a probability model and use it to find probabilities of events; compare probabilities from a model to observed frequencies

CCSS.7.SP.C.7a

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events

Grade 7

Quoted from the Common Core State Standards.

Where this sits

Comes after

Approximate Probability from Experimental Data

Leads to

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 7

This is one rung of 40 in Grade 7 mathematics, in the order they build on each other.

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