Subway trains on a certain line runs every half hour between midnight and six in the morning. What is the probability that the men entering the station at random time during the period will have to wait at least 20 minutes.
2026-03-31 19:13:38.1774984418
This is a probability question once asked in gate exam can anyone please solve this
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The wait time will be a uniform distribution on the interval $[0, 30]$, meaning $f(x) = \frac{1}{30}$. A man will have to wait at least $20$ minutes if he arrives at a time in the interval $[0, 10]$, meaning the probability would be $$\int_{0}^{10}f(x)dx = \int_{0}^{10}\frac{1}{30}dx = \frac{1}{3}$$