Question

The number of traffic accidents occurring on any given day in Coralville is Poisson distributed with mean 5. The probability that any such accident involves an uninsured driver is 0.25, independent of all other such accidents. Calculate the probability that on a given day in Coralville there are no traffic accidents that involve an uninsured driver.

The answer will be 0.287, which I got 0.25

could someone willing to help thank you very much

Answer 1

Number of accidents follows poisson distribution with mean 5

Probability that accident involves an uninsured driver is 0.25

Since, the events are independent,

Number of accidents involves an uninsured driver is = 5*0.25 = 1.25

Therefore, Number of accidents involves an uninsured driver be Y and follows Poisson distribution with mean 1.25

Hence, Probability of no accident that involve an uninsured driver = P[ Y = 0 ] =( exp(-1.25)*)1.25)^0 )/0_factorial=

exp(-1.25) = 0.287 (approx)