Cut the Cards

[Albert Chan]

(07-30-2020 08:00 PM)David Hayden Wrote:  Choose a card at random from a deck of 52 and put the card back.
What is the average number of choices required to see all 52 cards?

First card picked must never been seen, thus only 1 try needed to get 1st card.
Probability of getting the next "new" card = 51/52, or averaged 52/51 tries to get 2nd card
...

We can get averaged picks either way:

XCas> sum(1/t, t=1 .. 52) * 52.0                 → 235.978285436
XCas> int((t^52-1)/(t-1), t=0 .. 1) * 52.0    → 235.978285436

→ averaged 236 picks to see all 52 cards