Another probability question, I've just started doing stats and probability, I've already done 23 questions now haha, this is number 42 in a longgggg list of examples im trying to master to form a masterbook so i can solve most problems . I've got as far as defining what I know etc, i.e. P(XA)=0.02 (probability that X has accident) any help would be cool(c) What is the probability of a new client having no accidents in their first 5 years?
An insurance company classifies drivers as class X, Y or Z. Experience indicates that the probability a class X driver has at least one accident in any one year is 0.02, while the corresponding probabilities for Y and Z are 0.04 and 0.1 respectively. The class of a new driver who applies to them for cover is not known, but from experience they have found that
30% of applicants are class X, 60% are class Y , and 10% are class Z.
(a) What the the probability of a new client having an accident in their first year?
(b) If a new client has no accidents in their first year, what is the probability that they are a class X driver?