If he has the pocket pair, then you're always going to see what you want to see.
If he doesn't have the pocket pair, then either (a) he would prefer you to see he had it or (b) he would prefer you to see he didn't have it.
In case (a),
1) If you've chosen, then you've got a 50% chance of seeing the card you want. If he's chosen, then you've got a 100% chance of seeing the card you want.
In case (b),
1) If you've chosen, then you've got a 50% chance of seeing the card you want. If he's chosen, then you've got a 0% chance of seeing the card you want.
I can't work it out now because I'm off to bed, but there might be some way of drawing up a tree diagram which goes through the eight possibilities and comes up with an appropriate function. Possibly I will have a go at this tomorrow.
I'm sure I had a point with question 2 at the time, but I can't remember what it was and on reflection it may well not make a difference.
no subject
If he doesn't have the pocket pair, then either (a) he would prefer you to see he had it or (b) he would prefer you to see he didn't have it.
In case (a),
1) If you've chosen, then you've got a 50% chance of seeing the card you want. If he's chosen, then you've got a 100% chance of seeing the card you want.
In case (b),
1) If you've chosen, then you've got a 50% chance of seeing the card you want. If he's chosen, then you've got a 0% chance of seeing the card you want.
I can't work it out now because I'm off to bed, but there might be some way of drawing up a tree diagram which goes through the eight possibilities and comes up with an appropriate function. Possibly I will have a go at this tomorrow.
I'm sure I had a point with question 2 at the time, but I can't remember what it was and on reflection it may well not make a difference.