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AP EAMCET · Maths · Probability

If the average number of accidents occuring at a particular junction on a highway in a week is 5, then the probability that atmost one accident occurs in a particular week is

  1. A \(\frac{25}{\mathrm{e}^4}\)
  2. B \(\frac{24}{e^4}\)
  3. C \(\frac{121}{e^5}\)
  4. D \(\frac{6}{e^5}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{6}{e^5}\)

Step-by-step Solution

Detailed explanation

\(P(X \le 1) = P(X=0) + P(X=1)\) \(P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}\) \(P(X \le 1) = \frac{e^{-5} 5^0}{0!} + \frac{e^{-5} 5^1}{1!}\) \(P(X \le 1) = e^{-5} + 5e^{-5}\) \(P(X \le 1) = 6e^{-5} = \frac{6}{e^5}\)