This should be very easy, but I can't get the idea of counting this right:
So I have a stack of 100 cards. 21 of those says "HIT" and 79 says "MISS". What are the odds to take 32 random cards and have 30 of those saying "MISS" and 2 saying "HIT"? The cards are not put back on the stack after pulling one out ie. after that 32nd card there's only 68 left.
I tried to begin this by creating a simple table in "X cards, Y hits" way, but I was only able to get thru the first row (or having a stack of only one card) with knowing that it has to be correct: 79% for "MISS", 21% for "HIT". Then on the second row (or having a stack of only two cards) I'm pretty sure that the "Miss both" is (79/100)*(78/99)=62.24% and "Hit both" is (21/100)*(20/99)=4.24%, but I can't seem to get that one with "Hit one or the other, but not both" correct. I think it should be (79/100)*(21/99)+(21/100)*(78/99)=33.30%, but it seems to make the sum of these three cases to only 99.70% while it should be 100% (you can either hit one, both or neither).
So what's the formula to solve these and what's the actual probability to that "HIT 2 of 32"?
Thanks in advance for anyone trying to help me with this!