This is going way off topic, but anyway.
The events are not independent. If the first 51 cards are in their places, the probability of the card 52 being in its place is 1. | [reply] |

*If the first 51 cards are in their places, the probability of the card 52 being in its place is 1*
Yes, that's one scenario that will see the 52 card in its correct place - but, having shuffled a pack, the chance that the 52 card will be in its place is 1 in 52.
To determine the probability of a specific card being in a specific position one does not need to concern oneself with what might be in the other positions.
Consider a deck of 3 cards - say 2 of hearts, 3 of hearts and 4 of hearts. Let's designate that the correct position for the 2 of hearts is the top of the deck, the correct position for the 3 of hearts is the middle of the deck and the correct position for the 4 of hearts is the bottom of the deck.
Clearly the chance of the 2 of hearts being in its correct place after shuffling is 1 in 3(same as for the other 2 cards). The fact that that the 2 of hearts *has* to be in its correct place if both the 3 & 4 of hearts are in their correct places doesn't warrant any special consideration ... that I can see, anyway.
Cheers, Rob
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*The fact that that the 2 of hearts *has* to be in its correct place if both the 3 & 4 of hearts are in their correct places doesn't warrant any special consideration ... that I can see, anyway. *
I was with you until that last sentence, which I don't get. There is a difference between sampling with replacement and sampling without replacement. I would argue that checking *all* of the cards in the deck, instead of just one, is sampling without replacement: Once the position of the first card has been checked, there are only 51 cards in 51 possible positions remaining, and so on.
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