How do you find the answer to the following question: An insurance company classifies drivers as low-risk, medium-risk, and high-risk. Of those insured, 60% are low-risk, 30% are medium-risk, and 10% are high-risk. After a study, the company finds that during a 1-year period, 1% of the low-risk drivers had an accident, 5% of the medium-risk drivers had an accident, and 9% of the high-risk drivers had an accident. If a driver is selected at random, find the probability that the driver will have had an accident during the year.
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March 11, 2010 @ 5:01 am
60% * 1% + 30% * 5% + 9% * 10% =
(.6 * .01) + (.3 * .05) + (.1 * .09) =
.006 + 0.015 + 0.009 = .03 * 100 = 3%
March 11, 2010 @ 5:39 am
P(L) = .6 P(M) = .3 P(H) = .1
P(A|L) = .01 P(A|M) = .05 P(A|H) = .09
Using the formula of total probability,
P(A) = P(A|L)P(L) + P(A|M)P(M) + P(A|H)P(H)
= (.01)(.6) + (.05)(.3) + (.09)(.1)
= .03