If you take P(win)^attempts, that gives you the probability of winning on every single attempt, which is going to be much lower than the probability of winning one attempt. To find probability of winning at least once over 10 tries it is easier to find the converse (probability of losing every time) and subtract it from 1.
1-((1-0.0002)^10) = 0.0019 or about 2%
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