Question

A hand of five cards is dealt - randomly one card at a time, without replacement - from each of the two standard decks of 52 cards.?
1. What is the probability that the two hands have exactly one card in common?
2. What is the probability that the two hands have at least one card in common?

Answer 1

answer to one is two in 104
answer to two is two in104
those are my best guesses

Answer 2

Could you explain how you get those answers?

Answer 3

The probability that a particular card is the same in both hands is given by:
\[P(1\ card\ the\ same)=\frac{51 \choose4}{52 \choose5}=\frac{5}{52}\]
The probability that a particular card is different in both hands is given by:
\[P(1\ card\ is\ different)=\frac{51 \choose5}{52 \choose5}=\frac{47}{52}\]
\[P(1\ card\ is\ common,\ 4\ cards\ different)=\frac{5\times47\times47\times47\times47}{52\times52\times52\times52\times52}\]