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Probability

Section: Mathematics

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Question : 18 of 92

Marks: +1, -0

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

[AP EAPCET 23 May 2025 S1]

$\;\frac{25}{e^4}$
$\;\frac{24}{e^4}$
$\;\frac{121}{e^5}$
$\;\frac{6}{e^5}$

Solution:

Average number of accidents per weeks

(\lambda)=5

We want to find the probability of at most one accident i.e.

P(X \leq 1)=P(0)+P(1) .

As we know that, poisson probability formula,

P(X=k)=\;\frac{e^{-\lambda} \lambda^k}{k!}

\therefore \;\; P(0)=\;\frac{e^{-5} \cdot 5^0}{0!}=e^{-5}

P(1)=\;\frac{e^{-5} \cdot 5^1}{1!}=5 e^{-5}

\therefore P(X \leq 1)=e^{-5}(1+5)=6 e^{-5}=\;\frac{6}{e^5}

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