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TS EAMCET · Maths · Probability

An observer counts 240 vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at the location follows Poisson distribution, the probability that more than two vehicles arrive over a 30 sec time interval is

  1. A \(\frac{e^2-5}{e^2}\)
  2. B \(\frac{e^2-2}{e^2}\)
  3. C \(\frac{1}{12 e^2}\)
  4. D \(\frac{12-e^2}{e^2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{e^2-5}{e^2}\)

Step-by-step Solution

Detailed explanation

The average arrival rate, \(\lambda\) is \(240 \mathrm{veh} / \mathrm{h}\) or \(1 / 15\) vehicles per second. According to poisson distribution, \(P(n)=\frac{(\lambda t)^n e^{-\lambda t}}{n !}\) Where, \(P(n)=\) probability of having \(n\) vehicles arrive in time \(t\),…