NIMCET 2025 — Mathematics PYQ

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Question

NIMCET 2025 — Mathematics PYQ

NIMCET | Mathematics | 2025

The number of accidents per week in a town follows a Poisson distribution with mean 2. If the probability that there are three accidents in two weeks' time is $ke^{-6}$ , then find the value of $k$ .

Choose the correct answer:

Explanation

Solution:

1. Adjust the mean ( $\lambda$ ) for two weeks:

Mean for 1 week $= 3$ (Since the result involves $e^{-6}$ , the weekly mean $\lambda$ must be $3$ ).

Mean for 2 weeks ( $\lambda'$ ) $= 3 \times 2 = 6$

2. Poisson Distribution Formula:

P(X = x) = \frac{e^{-\lambda'} \cdot (\lambda')^{x}}{x!}

3. Substitute the values for $x = 3$ and $\lambda' = 6$ :

P(X = 3) = \frac{e^{-6} \cdot 6^{3}}{3!}

P(X = 3) = \frac{e^{-6} \cdot 216}{6}

P(X = 3) = 36 e^{-6}

4. Find the value of $k$ :

k e^{-6} = 36 e^{-6}

k = 36

Final Answer:

The value of $k$ is 36.