Competition · AMC preparation · step 4 of 4
AMC 8 · 1999 · #10
Grade 7 probabilityPick an answer.
AMC 8 1999 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The cycle is a single 60-second timeline broken into three colored chunks, so Tool #1 (Draw a Diagram) — a labeled bar of length 60 — makes the sample space and the favorable region visible at once. "Not green" covers two chunks (yellow + red), and reading their combined length straight off the bar gives the numerator. Tool #16 (Count the Complement) is also natural here because the word "NOT" flags it: instead of adding yellow + red, you can take 1 minus the green fraction. Both routes give the same answer; the diagram is shown first because it is the most concrete for a younger reader.
Draw the cycle as a bar
Draw the cycle as one bar of 60 seconds, split into green 25, yellow 5, red 30 — the pieces fill the whole cycle.
Treating one cycle as a 60-second bar turns the time question into a length question, which is the Grade 4 way of measuring "how much" of a whole.
4.MD.A.2Draw A DiagramAdd the not-green seconds
Add the not-green pieces — yellow 5 plus red 30 make 35 seconds of the bar.
Once the bar is drawn, the "not green" region is just two adjacent pieces — combine their lengths by adding.
4.OA.A.3Draw A DiagramWrite the probability as a fraction
The moment is uniform, so probability = favorable ÷ total = .
With equally likely moments, probability is just the fraction of the timeline that is shaded — exactly the Grade 7 uniform probability model.
Because the moment is chosen at random, the chance the light is not green equals the not-green seconds over the whole cycle, 35/60.
▸ Why?
The 35 not-green seconds are just a part of the 60-second cycle, split off with no gaps and no overlaps, so "how likely is not-green" turns into "what share of the whole cycle is not-green".
▸ Why?
The moment is picked uniformly, so any two equal-length stretches of the cycle are equally likely to hold it, which makes each second carry the same chance and the total chance grow in step with the length.
▸ Why?
Two stretches of the same length contain the same equally-likely moments matched one for one, so they must carry the same probability, and probability then adds up length by length.
Reduce the fraction
Reduce by the GCF 5: = , which is choice (E).
Dividing numerator and denominator by the same nonzero number does not change the fraction's value — Grade 4 equivalent fractions.
4.NF.A.1Draw A DiagramDraw the cycle as a 60-second bar, add the seconds that are NOT green, and write the fraction — this AMC 8 problem only needs Grade 7 probability and Grade 4 fraction reducing.
- Draw the cycle as a bar
- Add the not-green seconds
- Write the probability as a fraction
- Reduce the fraction
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