An insurance company divides it's customers into 2 groups. 20% of the customers are in the high risk group, and 80% are in the low risk group. High risk customers have 1 wreck compared to low risk drivers wrecking 0.1 times a year.If a driver has no wrecks, what's the probability that the driver is high risk?
I originally approached this problem using Bayes Rule but quickly realized I don't know how to find the probability of 0 wrecks from an average.
So, I moved on to trying Poisson Distribution with \lambda = .1 and x = 0 but that returns .36 while the book shows .0923.
Best Answer
I got .0923 with Poisson distribution. $\frac{0.2*e^{-1}}{0.2*e^{-1}+0.8*e^{-0.1}}$.