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Describe probability from impossible to certain

Probability describes the likelihood of an event on a continuum from impossible to certain: an impossible event has probability 0, a certain event has probability 1, and other events lie between them. Learners interpret and compare simple random events using terms such as unlikely, equally likely, and likely, representing likelihood with fractions, decimals, percentages, or a 0–1 number line; conditional probability and advanced probability models are outside this scope.

Detailed Explanation: Describe probability from impossible to certain

Probability tells how likely something is to happen. It ranges from:

  • 00: impossible
  • Between 00 and 11: possible
  • 11: certain

A probability can be written as a fraction, decimal, or percentage. For example,

12=0.5=50%.\frac{1}{2}=0.5=50\%.

Worked example

A spinner has 88 equal sections:

  • 33 red sections
  • 44 blue sections
  • 11 yellow section

Find and describe the probability of each event.

1. Landing on red

There are 33 red sections out of 88 total sections, so

P(red)=38=0.375=37.5%.P(\text{red})=\frac{3}{8}=0.375=37.5\%.

This event is possible but less than half as likely, so landing on red is unlikely.

2. Landing on blue

There are 44 blue sections out of 88 total sections:

P(blue)=48=12=0.5=50%.P(\text{blue})=\frac{4}{8}=\frac{1}{2}=0.5=50\%.

Landing on blue is equally likely as not landing on blue because the probability is exactly one-half.

3. Landing on yellow

There is 11 yellow section out of 88:

P(yellow)=18=0.125=12.5%.P(\text{yellow})=\frac{1}{8}=0.125=12.5\%.

This is a small probability, so landing on yellow is unlikely.

4. Landing on purple

There are no purple sections:

P(purple)=08=0.P(\text{purple})=\frac{0}{8}=0.

Landing on purple is impossible.

5. Landing on red, blue, or yellow

Every section is red, blue, or yellow, so this event must happen:

P(red, blue, or yellow)=88=1.P(\text{red, blue, or yellow})=\frac{8}{8}=1.

This event is certain.

You can picture these probabilities on a number line:

0⟶12⟶10\quad\longrightarrow\quad \frac{1}{2}\quad\longrightarrow\quad 1

Impossible events are at 00, certain events are at 11, and all other events are somewhere between them. A larger probability means an event is more likely.

Learn by doing: Describe probability from impossible to certain

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