Problem-Solving and Data AnalysisVery hardComplement of all failing
Problem-Solving and Data Analysis practice question
A building has three independent smoke alarms, and each has a probability of 1/5 of failing during a fire. What is the probability that at least one alarm works during a fire?
Answer: 124/125 or 0.992
P(all three fail) = (1/5)³ = 1/125, so P(at least one works) = 1 − 1/125 = 124/125.
Common wrong answers
- If you answered 1/125
- 1/125 is the probability that every alarm fails.
- If you answered 4/5
- 4/5 is the probability that one particular alarm works.
- If you answered 64/125
- 64/125 is the probability that all three work, which is not what "at least one" asks.
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