Problem 10 · 1999 AMC 8
Medium
Counting & Probability
probability
A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds, and red for 30 seconds. At a randomly chosen time, what is the probability that the light will NOT be green?
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Answer: E — 7/12.
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Hint 1 of 2
Probability over time = (favorable seconds) ÷ (total seconds). The favorable event is "not green" — so which seconds count?
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Hint 2 of 2
"Not green" is the opposite of green. You can add up yellow + red, or just take the whole cycle minus the green time — the complement trick.
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Approach: favorable time over total — or 1 minus the green probability
- A random instant is equally likely anywhere in the 60-second cycle, so probability = (matching seconds) ÷ 60.
- "Not green" = yellow + red = 5 + 30 = 35 seconds, giving 35/60 = 7/12.
- Complement shortcut: green is 25/60, so not-green is 1 − 25/60 = 35/60 = 7/12 — same answer. Whenever the "not" event has fewer pieces to add, subtract from 1 instead.
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