A practical question. Given two decks of cards (52 cards) if i pick 15 cards randomly from one deck and then 5 cards from another deck, what is the probability that exactly 3 cards, between two picked sets, will be same ? What is the probability that at least 3 cards will be the same?
Thank you so much !!
Apendix: added on 31.12.13
let me see if i got this right. if i modify the above example so that i am returning my picked cards back to the deck (sampling with replacement) then once i pick 15 cards i count the number of different cards which gives me the probability for picking a matched card from the second deck. thherefore i have :
$p(pick)=15/52 $
$q(not\_pick) = 1-15/52$
and then :
my probability for picking a matching pair is $\binom {5} {2}p(pick)q(not\_pick) \times \binom {5} {2} p(pick)q(not\_pick) \times \binom {5} {2} p(pick)q(not\_pick)$
or did i messed up again??
and thank you so much for all your help 🙂
Best Answer
$\textbf{Hint:}$ There are two decks. You are trying to find three cards that are exactly the same.