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I am trying to answer my own question of
"If I have a 30 card deck with 28 unique cards and 2 identical cards of interest, what are the odds of drawing one of the 2 identical cards in the first 7?"
I understand that the odds of drawing one of the unique cards in the first 7 is expressed as
29c6 / 30c7
where NcK is "N choose K" or Binomial[N,K] in Mathematica.
Am I correct in using the following to answer my original question?
Let q be the first card of interest and q' be the second:
P(q or q') = P(q) + P(q')  P(q and q')
which in the case of identical cards of interest becomes:
P(q or q') = 2*P(q)  P(q and q')
and the probability of P(q and q') is the following:
Binomial[28,5] / Binomial[30,7]
thereby giving a solution to my original question
P(q or q') = 2* ( Binomial[29,6] / Binomial[30,7] )  ( Binomial[28,5] / Binomial[30,7] ) = 0.4183
29c6 / 30c7
where NcK is "N choose K" or Binomial[N,K] in Mathematica.
Am I correct in using the following to answer my original question?
Let q be the first card of interest and q' be the second:
P(q or q') = P(q) + P(q')  P(q and q')
which in the case of identical cards of interest becomes:
P(q or q') = 2*P(q)  P(q and q')
and the probability of P(q and q') is the following:
Binomial[28,5] / Binomial[30,7]
thereby giving a solution to my original question
P(q or q') = 2* ( Binomial[29,6] / Binomial[30,7] )  ( Binomial[28,5] / Binomial[30,7] ) = 0.4183