A pioneer was panning gold in Qinhai and only 2% chance on the average that he found gold in the past many years. What is the chance for him to find gold in 28 pans or more out of the next 1000 trials?

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I wonder if I should use the binomial probability to obtain the answer. If so, does it mean that I have to calculate all the 28 probabities to do it?

p = 0.02, q = 0.98

1 - (q^1000 + 1000*q^999*p + 499500*q^998*p^2 + ... )