I have the following question from a book.
A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is?
And the solution to this is:
The problem can be done using binomial distribution since the population is infinite.
Probability of defective item $p=0.1$. Probability of non-defective item $q=0.9$. Probability that exactly 2 of the chosen items are defective:
Now my doubt is how can the probability of the new random section of 10 items have the same as that of the bigger (infinitely in this case, although I would prefer a general answer) set? Suppose we coincidentally get 10 defective items then the probability of the lot of 10 having defective items would be $100 \%$, right?
Can someone please explain to me if the solution is wrong or I am missing something here?