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0
\(\frac{1}{2}\)
 1

Probability:
A Number from \(0\) to \(1\)

Learn how every chance event has a probability between \(0\) and \(1\), and what that number tells you about how likely the event is to happen.

7th Grade Math

What Is Probability?

Probability is a number that measures how likely something is to happen. We write probability as a value from \(0\) to \(1\).

Impossible
Probability = \(0\). The event cannot happen.
Equally Likely
Probability = \(\frac{1}{2}\). Could go either way.
Certain
Probability = \(1\). The event will definitely happen.

The Probability Scale

0 0.25 0.5 0.75 1 Impossible Unlikely Even Chance Likely Certain

Why Does Probability Matter?

We use probability every day, often without realizing it. Understanding the scale from \(0\) to \(1\) helps us make better decisions about uncertain situations.

Weather
A 90% chance of rain means \(P = 0.9\): very likely, so bring an umbrella.
Games
Rolling a 6 on a die: \(P = \frac{1}{6} \approx 0.17\): unlikely on any single roll.
Sports
A free-throw shooter hitting 80% has \(P = 0.8\): likely to make the next shot.

The Core Rule of Probability

[ ] 0
\(\frac{1}{2}\)
 1 Impossible Neither unlikely nor likely Certain Increasing Likelihood →

Calculating Probability

This formula always gives a result between \(0\) and \(1\), because favorable outcomes can never exceed total outcomes.

Unlikely vs. Likely vs. Even Chance

Region Probability Range What It Means
Near 0 \(0 \le P < 0.3\) Unlikely: event probably won't happen
Around \(\frac{1}{2}\) \(0.3 \le P \le 0.7\) Neither unlikely nor likely: could go either way
Near 1 \(0.7 < P \le 1\) Likely: event will probably happen

How to Find a Probability

1
Identify the event. What outcome are you interested in?
2
Count favorable outcomes. How many ways can the event happen?
3
Count total outcomes. How many outcomes are possible altogether?
4
Divide. Compute \(P(E) = \frac{\text{favorable}}{\text{total}}\).
5
Interpret. Is the result near \(0\), near \(\frac{1}{2}\), or near \(1\)?

Example 1: Flipping a Coin

H Heads T Tails

Example 2: Spinning a Spinner

1 2 3 4 4 equal sections P(landing on 3) = ? Favorable: 1 Total: 4
\(P = \frac{1}{4} = 0.25\)

Example 3: Drawing a Marble

= 7 green = 3 red Total: 10
\(P(\text{green}) = \frac{7}{10}\)

The Extremes: \(0\) and \(1\)

\(P = 0\): Impossible
Rolling a 7 on a standard 6-sided die. There is no 7, so there are zero favorable outcomes: \(\frac{0}{6} = 0\).
\(P = 1\): Certain
Rolling a number less than 7 on a standard die. Every face qualifies: \(\frac{6}{6} = 1\).

Placing Events on the Scale

0 0.5 1 Rolling a 7 P = 0 Rolling a 6
\(P = \frac{1}{6}\)
 Coin heads
\(P = \frac{1}{2}\)
 Green marble
\(P = \frac{7}{10}\)
 Number < 7 P = 1

Each event we've seen fits on the probability number line. Compare positions to compare likelihoods.

Three Ways to Express Probability

Event Fraction Decimal Percent
Coin lands heads \(\frac{1}{2}\) \(0.5\) \(50\%\)
Rolling a 3 on a die \(\frac{1}{6}\) \(0.1\overline{6}\) \(\approx 16.7\%\)
Drawing green marble \(\frac{7}{10}\) \(0.7\) \(70\%\)
Drawing red marble \(\frac{3}{10}\) \(0.3\) \(30\%\)

Common Mistakes to Avoid

✕ Probability Over 1
Writing \(P = \frac{8}{5} = 1.6\). Probability can never exceed \(1\): check that \(\text{favorable} \le \text{total}\).
✕ Negative Probability
Stating \(P = -0.2\). Probability is always \(\ge 0\). If you get a negative, recount your outcomes.
✕ Confusing "Unlikely" with "Impossible"
An event with \(P = 0.05\) is unlikely but not impossible. Only \(P = 0\) means truly impossible.

Question 1 of 5

A bag contains 4 blue and 6 yellow marbles. What is the probability of drawing a blue marble?

Question 2 of 5

Which probability describes an event that is unlikely but not impossible?

Question 3 of 5

A spinner has 8 equal sections numbered \(1\) through \(8\). What is \(P(\text{landing on an even number})\)?

Question 4 of 5

Event A has \(P = 0.85\) and Event B has \(P = 0.3\). Which statement is correct?

Question 5 of 5

A student says the probability of picking a red card from a standard deck is \(\frac{26}{52}\). What does this probability tell us about the event?