# Actuarial Science - Part 1

There are two types of driver. Good drivers make up $$75\text{%}$$ of the population and in one year have zero claims with probability $$0.7$$, one claim with probability $$0.2$$, and two claims with probability $$0.1$$. Bad drivers make up the other $$25\text{%}$$ of the population and have zero, one, or two claims with probabilities $$0.5,\,0.3,$$ and $$0.2$$, respectively. For a particular policyholder suppose that an actuary has first observation zero claims and second observation one claim. The probability that the third observation more than or equal to one claim given that the previous observations can be expressed as $$\,\dfrac{p}{q}$$. Calculate $$p+q$$.

Details and assumptions :

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