Polya Urn After Ten Draws

An urn starts with 1 white ball and 1 black ball. Each second you draw one ball uniformly at random, put it back, and add one more ball of the colour you just drew, so the urn grows by one ball every second.

You watch the first 10 draws. What is the probability that exactly 7 of them were white? Answer format: round to 3 decimal places.