In: Statistics and Probability
An insurance company divided its clients into two categories, amateur and professional. The last year accident report shows 10% of amateur drivers and 2.5% of professional drivers are involved in an accident. If 15% of drivers are amateur license and 85% are professional, find the following probabilities. For simplicity, assume year to year accident accidents for any driver are independent.
here let say
Amateur Driver = A
so, P(A) = 0.15
Professional Drive = B
so, P(B) = 0.85
Now if Getting accident done is Cthen
it is also given
P(Amateur Driver do accident) = P(C l A) = 0.10
P(Professional Driver do accident) = P(B l A) = 0.025
(a) P(Accident of a driver) = P(C) = P(C l A) * P(A) + P(C l B) * P(B)
= 0.10 * 0.15 + 0.025 * 0.85 = 0.03625
(b) P(An amateur driver is involved in at least one accident during 3 years) = 1 - P(No accident in 3 years)
=1 - (1 - 0.10)3 = 0.271
(c) P(Not having an accident for a professional driver during 3 years) = (1 - 0.025)3 = 0.9269
(d) Here annual insurance premium is computed according to being involved to at least one accident in 3 years
as we know
P(Amateur driver had at least one accident in 3 years) = 0.271
P(Professional Driver has at least one accident in 3 years) = 1 - 0.9269 = 0.07314
so here more probability of accident means more premium. Let say the premium of Amteur driver is X.
so here value of the premium is proportion to probability of accident/ (1 - probability of accident)
X/1000 = [(0.271/(1 - 0.271)/(0.07314/(1 -0.07314)]
X = $ 4711