Probability of failure needed

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There are 38 numbers on a wheel. I pick 5 numbers and maintain those 5 numbers for 35 spins of the wheel. What is the probability that 1 of my 5 numbers will NOT be selected within the 35 spins/rounds? I know the math equation and answer for this is 0.0072 failure rate...NOW... the answer I need now is...how many times can I expect my 35 round system to succeed before failing?