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Understand Probability as a Number from 0 to 1

Students understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. They interpret probability values close to 0 as unlikely, close to 1 as likely, and ½ as equally likely and unlikely.

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Understand Probability as a Number from 0 to 1

Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

2 of 10 equally likely outcomes: P = as a decimal

How it is taught

0:00 of 3:57

Probability is a number from 0 to 1 that names how likely an event is.

0 means it cannot happen; 1 means it must happen.

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.

15 of 40 equally likely outcomes: P = ___ — 0.375. P is the event's part of all 40: 15 ÷ 40 = 0.375.

Placing events on the probability line

How do we measure how likely something is to happen? Mathematicians use a number called probability.

Every probability lives on a number line that goes from zero to one.

Zero means impossible. The event can never, ever happen.

One means certain. The event is guaranteed to happen.

One-half is right in the middle — the event is equally likely to happen or not.

Roll a seven on a regular six-sided die? That's impossible — probability zero.

Roll a one? There's only one way out of six, so the probability is one-sixth, about 0.17 — unlikely.

Roll an even number? Three of six sides work, so the probability is one-half — equally likely.

Roll less than six? Five of six sides work, so the probability is five-sixths, about 0.83 — likely.

Roll any number from one to six? That's certain — probability one.

The closer a probability is to zero, the less likely. The closer to one, the more likely.

Every probability is a number between zero and one — that's all you need to compare how likely things are.

How likely is it?Probability is a number from 0 to 1The probability line0112ImpossibleCertainEqually likelyRolling a 7 on a six-sided dieP = 0Rolling a 1: 1 out of 6≈ 0.17Rolling an even number: 3 out of 6= 0.5Rolling less than 6: 5 out of 6≈ 0.83Rolling 1, 2, 3, 4, 5, or 6P = 1← less likelymore likely →PROBABILITY0 → 1always between
Grade 7 · Likelihood lives between zero and 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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