I am trying to work out the expected value of the following example:
A data set contains 1000 examples in total. 10 examples can be considered anomalous.
I am randomly drawing 100 examples to form a batch.
I have two related questions.
1) What is the probability that a batch will contain 5 or more anomalies?
2) What is the probability that a batch will contain 1 or more anomalies?
I believe I need to calculate the combinations.
I can start by considering the probability that I draw no anomalies and taking the compliment. Let $X$ be the number of anomalies.
$P(X \ge 1 ) = 1 - P(X = 0)$, where $P(X = 0) = C(10,0) C(990,100) / C(1000,100) = 0.346 $ so $P(X \ge 1 ) = 0.653$
So 65.3% of the time a batch will contain at least one anomaly? I'm doubting myself because that seems so high.
For the probability of drawing at least 5 anomalies, I'm less sure where to begin.