An automobile insurance company issues a one-year policy with a deductible of $500$. The probability is $0.8$ that the insured automobile has no accident and $0.0$ that the automobile has more than one accident. If there is an accident, the loss before application of the deductible is exponentially distributed with mean $3000$. Calculate the $95$th percentile of the insurance company payout on this policy.
I found a solution online which begins with:
The $95$th percentile is in the range when an accident occurs. It is the 75th percentile of the payout, given that an accident occurs, because $(0.95 − 0.80)/(1 − 0.80) = 0.75$.
Can someone please explain what the author of the solution was trying to achieve by writing $0.95-0.80$. I think $(1-0.80)$ is the probability that an accident occurs.