You are the class president and have ordered 300 T-shirts for the grade from a clothing manufacturer that claims that it averages only five discolored T-shirts for every 50,000 T-shirts it produces. What is the probability that your order will contain one or more discolored T-shirts?

% (Round your answer to the nearest hundredth)

Using complements, we can simply find the probability that all the T-shirts are perfect and subtract this value from 1. The probability that any one given T-shirt is perfect is (50,000-5)/50,000=. Therefore, the probability that all 300 T-shirts that you ordered are perfect is

P(A)=(49995/50000)^{300}≈0.970444

So, the probability that at least one T-shirt is discolored is

P(A’)=1-P(A)=1-0.970444≈0.02955592≈2.96%