If it's a real, independent uniform random sampling, the probability of a sample of K people containing at least one such person is .
That's because the event of at least 1 having it is the complement of the event of no-one having it, which, in turn, is the intersection of K independent events: person 1 not having it, person 2 not having it, ..., person K not having it.
Of course, if the sampling is not uniform and independent, the probability could be different. And I don't know how to phrase this in terms of "odds" -- I'm not a gambler.
