Probability of same genes or cards. Let's say there is a deck of 100 cards, you choose 6 cards of them. Another person also choose 6 in a new deck.
What is the probability of sharing one card?
What is the probability of sharing two cards?
...
What is the probability of sharing 6 cards?
I couldn't figure out the distribution.
there are 100C6 ways of choosing 6 cards but a second person also has those possibilities. How do I know if the card is the same?
If it was only a single card for both, then there are 100 ways of 100^2 = 1/100.
With two cards for both...
Maybe taking off artificially 6 cards from the second deck, then 100C6*94C6= number of ways without repeating a single card.
Then $(100C6*94C6)/(100C6)^2=(94C6)/(100C6)=0.68$ is the percentage of no cards repeated and 1-ans is the probability of 1|2|3|4|5|6?
If yes, how do I find individual cases?
 A: You can rephrase like this:

There are $100$ cards and $6$ of them are marked. If someone picks $6$ of them randomly then what is the probability that among them there are exactly $k$ marked cards?

Think of it like this: you pick $6$ cards of the $100$ and mark them. Then the other person randomly picks $6$ of the cards.
The answer is gained by applying multihypergeometric distribution:$$\frac{\binom6k\binom{94}{6-k}}{\binom{100}6}$$
A: I am also learning probability recently, so here is my trial using hint from @JMoravitz, i.e. WLOG assume that $1$st person have already chosen cards $A,B,C,D,E,F$:
The probability that the second person shares only card $A$ with the first person:
$$P(\text{only card $A$ is shared})=\frac{{94\choose 89}}{{100\choose 6}}.$$
Then I guess to find out the probability that exactly $1$ card is shared (not necessarily card $A$), we need to multiply the above by ${6\choose 1}=6$.
So the answer for your first question I think: $6\times\frac{{94\choose 89}}{{100\choose 6}}$.
If this is true, the case when two people share exactly $2$ cards might calculated in similar way.
