Back to Understand that the probability of a chance event is a number between 0 and 1

Understanding Probability: The 0-to-1 Scale

Express probability answers as fractions, decimals, or percents. When asked to classify, use the labels: impossible, unlikely, equally likely/unlikely, likely, or certain.

Grade 7·21 problems·~35 min·Common Core Math - Grade 7·standard·7-sp-c-5

Work through problems with immediate feedback

Recall / Warm-Up

Which decimal is equal to $\\frac{1}{4}$ ?

$0.14$

$0.25$

$0.4$

$4.0$

Which fraction is greater: $\\frac{1}{3}$ or $\\frac{1}{5}$ ?

$\\frac{1}{5}$ , because 5 is greater than 3.

$\\frac{1}{3}$ , because dividing 1 into fewer pieces makes each piece larger.

They are equal.

Cannot be determined without a common denominator.

Express 40% as a decimal.

Error Analysis

A student is asked to find the probability of drawing a diamond from a standard 52-card deck. The student writes:

"There are 13 diamonds in a deck of 52 cards.
P(diamond) = 13/52 = 1/4 = 0.25.
Since 1/4 is one of the standard probability fractions we learned, this is a likely event."

The student computed the probability correctly. What error did the student make in the interpretation?

The student made an arithmetic error: $\\frac{13}{52} \\ne \\frac{1}{4}$ .

P = 1/4 = 0.25 is less than 0.5, which places it in the unlikely region — not likely. The student confused a 'common fraction' with a high probability.

The student should have used 13/52 without simplifying.

Drawing a diamond is actually an impossible event.

A bag contains only red and green marbles. A student is asked for the probability of picking a blue marble. The student writes:

"Blue is impossible — but actually it is worse than impossible. So P(blue) = −1."

Identify the two errors in the student's reasoning.

The student is correct — if something is impossible, a negative probability below 0 is appropriate.

Both errors: (1) Probability cannot be negative — the minimum is 0. (2) There is no such thing as 'worse than impossible.' P = 0 is the absolute floor; all impossible events have P = 0 regardless of how 'impossible' they seem.

The student should have written P(blue) = 0.001 instead of −1.

The student was right to write a negative value since there are no blue marbles.

Challenge

Design four probability events:
(a) One event with P = 0 (impossible)
(b) One event with P = 1 (certain)
(c) One event with P = 1/2 (equally likely/unlikely)
(d) One event with P approximately 1/4 (unlikely)

For each event: (i) write a specific, clearly described event, (ii) state the probability as both a fraction and a decimal, and (iii) classify it using the landmark labels (impossible / unlikely / equally likely / likely / certain).

A student estimates: "The probability that I get the next quiz question right is 0.7."

(a) Is 0.7 a valid probability value? Explain using the definition of probability.
(b) Classify 0.7 using the landmark labels (impossible / unlikely / equally likely / likely / certain).
(c) The student adds: "So the probability I get it wrong is 0.4." Explain whether this is consistent with the rules of probability, and what the correct value should be.

0 of 21 answered

Understanding Probability: The 0-to-1 Scale

Recall / Warm-Up

Fluency

Varied Practice

Word Problems

Error Analysis

Challenge