If I choose four cards from a standard 52-card deck,with replacement, what is the probability that I will end up with all four Aces?
Each time you draw a card you have a 4/52 chance of an ace (or 1/13 chance)
.....what is the probability that I will end up with all four Aces?
By this, do you mean
...probability that I will have pulled an ace each time?
...probability that I will have pulled the ace of each suit?
Good point.....questions are often unclear and subject to interpretation by the answerer.
If you want to get EACH of the aces it would be a little more difficult :
I think it would be 4/52 for the first ace, which could be any of the four aces
and then 3/52 for an undrawn ace, one of the remaining three
and then 2/52 for one of the two remaining undrawn aces
and then 1/52 for the last ace that hadn't been previously drawn
for the total probability multiply them together
4 3 2 1 24 3
–– x –– x –– x –– = –––––––– = ––––––––
52 52 52 52 7,311,616 913,952