# Are waiting times always going to be exponentially distributed?

I'm studying for CAS/SOA Exam P/1 and a question I have here is:

We have a portfolio of $20$ insurance policies. The number of claims per policy in a $3$-month period has a Poisson distribution with mean $\frac12$. It is assumed that all of the policies in the portfolio are independent. What is the probability that there is a wait of more than $\frac12$ month before a claim is made by any policy in the whole portfolio?

Now the solution says that the mean for one month is $\frac{10}{3}$ which I understand where that comes from but then it says that the waiting time is exponentially distributed. Is that usually how waiting time problems are? Exponentially distributed if it's not said?

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