An insurance company divides its customers into 2 groups. Twenty percent of customers are in the high-risk group, and eighty percent are in the low-risk group. The high-risk customers make an average of 1 accident per year while the low-risk customers make an average of 0.1 accidents per year. Eric had no accidents last year. What is the probability that he is a high-risk driver?

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Business

Madalynn

20 July, 16:11

An insurance company divides its customers into 2 groups. Twenty percent of customers are in the high-risk group, and eighty percent are in the low-risk group. The high-risk customers make an average of 1 accident per year while the low-risk customers make an average of 0.1 accidents per year. Eric had no accidents last year. What is the probability that he is a high-risk driver?

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Sullivan Villarreal · Answer 1

0.0923 or 9.23%

Explanation:

We have to use the Poisson distribution:

P (x) = (0.2 x e⁻¹) / [ (0.2 x e⁻¹) + (0.8 x e⁻⁰°¹) ]

e = 2.71828 (given) lambda = λ = 0.1

0.073578 / (0.073578 + 0.72387) = 0.073578 / 0.79744 = 0.092267 or 9.23%

The Poisson distribution is used to calculate the probability of occurrence of independent and random variables.