You have 2 standard 52 card decks of card that have been shuffled randomly. You turn over the top card from the first deck, and the top card from the second deck.

(i) what is the probability that the two cards match?

(ii)you keep turning over the top card on each deck until you have gone through the deck. How many matches do you find?

(iii)you have a thousand letters and envelopes addressed to people. The envelopes get mixed up and a secretary puts letters at random into the envelopes. How many letter do you expect to end up in the correct envelope?