Pregunta
A washing machine has the following cycle: soak for 15 minutes, wash for 30 minutes, and rinse for 10 minutes. If you approach the machine at a random during the cycle, what is the probability that the cycle will be in the rinse phase when you arrive at the machine? Round your answer to the nearest hundredth.
Ask by Johnson Garrett. in the United States
Mar 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The probability of arriving during the rinse phase is 0.18.
Solución
Let the total cycle time be
\[
T = 15 + 30 + 10 = 55 \text{ minutes}.
\]
The probability that you arrive during the rinse phase is given by the ratio of the rinse duration to the total cycle time:
\[
P(\text{rinse}) = \frac{10}{55} = \frac{2}{11} \approx 0.18.
\]
Thus, the probability rounded to the nearest hundredth is \(0.18\).
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Simplifique esta solución Bonus Knowledge
To find the probability that the washing machine is in the rinse phase when approached randomly, we first need to calculate the total duration of the cycle. The cycle duration consists of soaking (15 minutes), washing (30 minutes), and rinsing (10 minutes), which totals up to 55 minutes. Now, since the rinse phase lasts 10 minutes, we can determine the probability by dividing the duration of the rinse phase by the total cycle duration: \[ P(\text{rinse}) = \frac{\text{duration of rinse}}{\text{total cycle duration}} = \frac{10}{55} = \frac{2}{11} \approx 0.1818. \] Rounding to the nearest hundredth, the probability is approximately 0.18.
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