Answer to Question #207837 in Statistics and Probability for shritha

Question

     (iv) Records show that the probability is 0.000002 that a bike rider will have an accident while driving on the way of university through Biswamil. Using poisson distribution determine the probability that among 200,000 bike riders driven on the way of university through Biswamil, not more than one will have an accident. ( e^-0.4 = 0.67)                                                                                     

Answer 1

$P=0.000002 \\ n=200000$

Let X is the number of bike riders that have an accident.

Poisson distribution:

X~P(λ)

$λ = np = 200000 \times 0.000002 = 0.4 \\ P(X=x) = \frac{e^{-λ}λ^x}{x!} \\ P(X≤1) = P(X=0) +P(X=1) \\ = \frac{e^{-0.4} \times 0.4^0}{0!} + \frac{e^{-0.4} \times 0.4^1}{1!} \\ = e^{-0.4} + e^{-0.4} \times 0.4 \\ = 1.4 \times 0.67 \\ = 0.938$