In a standard $52$-card deck we change 8♧ with 10♤ and 9♧ with J♤ from another deck of cards. If we change another card, which card should we change (and to what card) to maximize the probability of getting two pairs?
Here is my answer: there are $9$ ordinary ($4$ cards), $2$ weak ($3$ cards) and $2$ strong ($5$ cards) ranks. If we change another card among the $9$ ordinary ranks with the same rank as these cards, that is $1,2,3,4,5,6,7,Q,K$, and not the same rank, we'll then maximize the chance a bit.
Does it sound correct?