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Ratios and Data 6-8 / Week 12 / Monday
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Week 12 · Probability and the Data Fair

Monday

Chance from 0 to 1
// Chance from 0 to 1, fair spinners, and your own data report
⏱ about 20 min

Monday: Chance From 0 to 1

Rocket spins a paper plate on the Numbers Desk. "Field Day spinner game! Land on blue and you win a sticker."

Raven studies the plate. "Four equal sectors. Two blue, one red, one green. What do you notice?"

"Blue is the biggest," Rocket says. "So blue wins most of the time. Almost always, probably."

Nova hovers over the plate. "How much of the plate is blue?"

Rocket counts. "Two sectors out of four. Half."

"So out of every two spins, about how many land on blue?" Nova asks.

"About one," Rocket says slowly. "Not almost always. Half the time."

"Half is 1/2," Raven says. "Chance has a number. Let us put every event on the scale from 0 to 1."

Rocket, Raven and Nova at the Numbers Desk with a paper plate spinner, a paper clip pointer and a tally sheet.

The probability scale

The probability of an event is a number from 0 to 1. It says how likely the event is to happen.

A probability of 0 means the event cannot happen. A probability of 1 means it is certain to happen.

A probability of 1/2 means the event is as likely to happen as not. Numbers near 0 are unlikely. Numbers near 1 are likely.

You can write a probability as a fraction, a decimal or a percent. 1/2, 0.5 and 50% all name the same chance.

ProbabilityWord for itExample on spinner A
0impossiblelanding on gold (there is no gold)
between 0 and 1/2unlikelylanding on red (1 of 4 sectors)
1/2an even chancelanding on blue (2 of 4 sectors)
between 1/2 and 1likelylanding on blue or red (3 of 4 sectors)
1certainlanding on red, blue or green

Equally likely outcomes

Spinner A has four equal sectors. Each spin is equally likely to stop on any one of them. Each sector is one outcome.

With equally likely outcomes, the probability of an event is the number of outcomes that fit divided by all the outcomes.

Blue fills 2 of the 4 sectors. The probability of blue is 2/4 = 1/2.

Red fills 1 sector. The probability of red is 1/4. Green is the same, 1/4.

Add them up: 1/4 + 1/2 + 1/4 = 1. Every spin lands somewhere, so the probabilities of all the outcomes add to 1.

Spinner A: four equal sectors, 1 red, 2 blue and 1 green, with a pointer.
SPINNER A
  • Read the question.
  • Tap your answer.
Spinner AWhat is the probability of landing on blue?
Spinner AWhat is the probability of landing on red?
Spinner AWhat is the probability of landing on red or green?
Spinner AWhat is the probability of landing on gold on spinner A?
LIKELY OR UNLIKELY?
  • Read the question.
  • Tap your answer.
The probability of red on spinner A is 1/4. What word fits?
The probability of blue on spinner A is 1/2. What word fits?
The probability that spinner A lands on red, blue or green. What word fits?
The probability of not landing on red is 3/4. What word fits?
StatementTrue or false?
A probability of 0 means the event is certain.?
A probability of 1/2 means an even chance.?
The probabilities of all the outcomes of a spinner add to 1.?
On spinner A, blue is more likely than red.?
A probability can be bigger than 1.?
WHY THIS EXERCISEPlacing every chance on the same 0 to 1 scale lets you compare any two events.
How many equal sectors does spinner A have? Type the number.
WHY THIS EXERCISEThe number of equally likely outcomes is the denominator of every probability on that spinner.
Try it
Name an event in your day that is impossible, one that is certain, and one that is about an even chance.
Place each one on a line from 0 to 1 in your Numbers Notebook.

Chance now has a number. Tomorrow you use that number to predict what 40 spins will do.