Probability question: names in hats

[robvalue]

Nice

Just to show why it is 8/9 for the first pick, to get someone from player 2 to 9:

Prob(1st pick) + Prob(own name)*Prob(2nd pick)

=8/10 + (1/10)*(8/9)

=8/10 + 8/90

=72/90 + 8/90

=80/90

=8/9

So it does act as if their own name just wasn't in the hat in the first place. It would have to, or else the probabilities for each of the remaining 9 names wouldn't add up to 1.