Percent loss covered on average with a deductible

Suppose you have auto insurance with a deductible of \$200, and with no restriction on maximal payment. The probability of a loss is 0.10, and suppose that the distribution of the loss is exponential with a mean of \$1000.

What percentage of the loss does the insurance cover on average? The answer in the back of the book is 57.4%, but I am not sure how to reproduce it. This is how I thought of doing the problem:

Say that \$1000 = 1 unit of money (for ease of calculation), so that the deductible$d = 0.20$The payment function may be described as $$r(X) = \begin{cases} 0, \quad \quad x \leq 0.20 \\ x-0.2, \quad x > 0.20 \end{cases}$$ where$x$is the realization of the stochastic variable $$X = \begin{cases} \xi, \quad p = 0.10 \\ 0, \quad p = 0.90 \end{cases}$$ Here,$\xi$is the exponentially distributed loss. Since we are taking \$1000 to be a single unit of money, this just has a mean of 1.