I have a batch of 50 items. There is an inspection pass/fail criteria and 3 out of 50 failed inspection.
How do I determine if I pick 10 random items from this batch of 50 the probability %age that I will pick at least 1 failed item?
So far I have: 3/50 = 6% bad items when I pick 10, I have 10 * 6% chance of picking a bad item = 60% chance I have at least 1 bad item in my picked 10.
But if I had more than 5/50 failed items, it goes beyond 100% chance of picking a bad item...this feels wrong. I feel like only when I get to 50/50 failed items should I get to a 100% chance of having at least 1 failed item in my selection of 10.