Puzzle a Day!

I'm about to test this! I have 10 pieces of paper with the numbers 1-10 written on, and then folded into very small squares so I can't see the numbers.
I'm going to put them on another piece of paper marked into 10 squares and see how many match!!
The things we do to delay going out in the rain.

..............and the answer is NONE.............which isn't the answer in the puzzle book.

Mean, median, or mode?

Just simple guess will do!

Since I reckon about a third of the time none will be in the right envelope, I'm guessing the average will be about 2.
It's a guess though, I can't think of an easy trick to calculate it.

There's a 1 in 10 chance of placing any one random letter into the correct envelope, but one seems an overly simple answer.

I did some very convoluted, and almost certainly wildly incorrect, maths based on a *very* vague (mis)recollection of the impact of repeated events on overall probabilities and was left with an average (mean) of 1.2. The mode was 1. And I'm too tired to work out the median!

Pretty confused by this one, even though it should be one of the most straightforward for anyone more mathematically competent!

It's a tricky one this as you have a random 1 in 10 chance of the first envelope being right, then 1 in 9 for the second, 1 in 8 etc. There is something niggling in the back of my mind on how to do it but I stopped maths at gcse and I'm currently too tired to bring the info from the back of my mind.

Would you like the answer?
Don't read this if you want to go on puzzling!

One!!
It is far more likely that one will end up in the correct envelope than all ten will be in the wrong envelope.

How many times would you have to do it to prove the probability was one? Get cracking veggie!

Once was enough, Vinny.