Distribution table, drawing tickets w/o replacement
I recently encountered this problem while studying for a test, and im having trouble understanding how to solve it.
A box contains 8 tickets. Two are marked 1, two marked 2, two marked 3, two marked 4. Tickets are drawn at random from the box without replacement until a number appears that has appeared before. let X be the number of draws that are made. Make a table to display the probability distribution of X.
Now, i dont need the actual table, i just need to know how the book comes up with the answer P(X = 2) = 5/35, P(X = 3) = 10/35 (it only gives a partial answer, those are the only two it gives.)
From my understanding, after drawing once from the box (and thus taking one out), the probability of the second draw being the match to the first would be 1/7. So the sequence of draws would be (1/8)*(1/7).
1/56 != 5/35...
What am i doing wrong here?