What is the probability of success?

Question

If I have 12 Possible questions, of which 5 are asked and I only need to answer 2 of them, what is the probability of my success (i.e., I am able to answer 2 of the 5 asked questions) if I learn 2 of the 12 questions, 3 of the 12, 4 of the 12 etc.

So far, I figure that if I learn 9, I have a 100% chance of success.

Thanks

Answer 1

Use the hypergeometric distribution: $Hg(5,R=\mbox{number of questions you learnt},12)$.

The hypergeometric distribution is useful when we have a population of $N$ individuals, with $R$ individuals having the characteristic we are looking for and with $n$ as the number of individuals of a sample.

For a random variable $X$ with hypergeometric distribution $$\mathbb P(X=x)= \frac{\binom{R}{x}\binom{N-R}{n-x}}{\binom{N}{n}}.$$