1. The problem states that autos arrive at a tollbooth at a rate of 50 autos per minute from 12:00 to 13:00. 2. We want to find the probability that the next auto will arrive within 3 seconds. 3. Since arrivals are at a rate of 50 autos/minute, convert this rate to autos per second: $$\lambda = \frac{50}{60} = \frac{5}{6} \text{ autos per second}$$ 4. Assuming arrivals follow a Poisson process, the time between arrivals is modeled as an exponential random variable with parameter $\lambda = \frac{5}{6}$. 5. The probability that the next auto arrives within 3 seconds is the cumulative distribution function (CDF) of the exponential distribution: $$P(T \leq 3) = 1 - e^{-\lambda \times 3} = 1 - e^{-\frac{5}{6} \times 3} = 1 - e^{-2.5}$$ 6. Calculate the numerical value: $$1 - e^{-2.5} \approx 1 - 0.0821 = 0.9179$$ 7. Therefore, the probability that the next auto arrives within 3 seconds is approximately 0.918.