Kind of a Monty Hall Problem

[Lestat]

I've seen this before somewhere, maybe it was on here. But nothing turned up when I searched. I'm admitting defeat. I'm obviously being stupid somewhere and I can't figure out where. I know someone here will quickly be able to figure it out....



<font color="blue"> You are on a tv quiz show. The host has two boxes.

In one box there are 50 slips of paper that say "you have won $1"

In the other box there are 50 slips of paper that say "you have won $1,000".

You can leave the slips as they are, or mix them any way you wish. You can put them all in one box or split them any way between the two boxes. You cannot discard or hide any of the slips.

When you are done, the show host will select one of the two boxes and at random select one of the slips of paper from that box showing your prize.

Can you increase your odds of winning the $1,000 from 50/50? If so how and what will your odds be?

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Oh, and for extra credit:



<font color="blue"> Prior to the time I retired, my wife used to drive me to the train station to go to work in the morning and pick me up at the train station the same time in the evening.

One day I got off work early and took an early train which got me to the train station one our early. My wife was shopping (of course) and her cell phone battery was dead. I could not reach her to come to pick me up one hour earlier than usual.

It was a nice day, so I decided to walk home. After a while I saw her driving to the station to pick me up and I stopped her, got in the car, and we went home. We got home 20 minutes earlier than the normal time we would have gotten home had I taken the usual train.

How long was I walking before she picked me up?

You don't need to know how fast she was driving, how far it is from home to the station, how fast I walked, etc. There is no trick. There is one correct answer.
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I did (I'm pretty sure) get this one.