The money in the hats

No, said the mother to her 14-year old son Kyle. I do not feel inclined to increase your allowance by 10$ per week. However, if you're willing to take a risk, I'll make you a sporting proposition.

What is it this time, Mom?

I happen to have ten crisp new one-dollar bills and ten crisp new ten-dollar bills. You may divide them anyway you please into two sets. We'll put one set into hat A and the other set into hat B. Then I'll blindfold you. I'll mix the contents of each hat and place each one on the table. You pick either hat at random and then reach into the hat and withdraw one bill. If it's a ten you may keep it.

And if it isn't?

You wash my van once a week for a month with no complaints.

Kyle agreed. How should he distribute the 20 bills into the two hats to maximize the probability of drawing a ten-dollar bill and what will that probability be?

-Ray.

Edit: Why where my double quotation marks striped away?

Originally posted by rgoudie
No, said the mother to her 14-year old son Kyle. I do not feel inclined to increase your allowance by 10$ per week. However, if you're willing to take a risk, I'll make you a sporting proposition.

What is it this time, Mom?

I happen to have ten crisp new one-dollar bills and ten crisp new ten-dollar bills. You may divide them anyway you please into t ...[text shortened]... imize the probability of drawing a ten-dollar bill and what will that probability be?

-Ray.

One $10 bill in one hat and all the rest in the other, I think!

Originally posted by rgoudie
No, said the mother to her 14-year old son Kyle. I do not feel inclined to increase your allowance by 10$ per week. However, if you're willing to take a risk, I'll make you a sporting proposition.

What is it this time, Mom?

I happen ...[text shortened]... g a ten-dollar bill and what will that probability be?

-Ray.
n

pure intuition: put one 10-dollar bill in one hat, the rest in the other.
His chances: 0.5x1 + 0.5x9:19 = 14/19 = 73.7%

edit: oops, too late!

You are both correct.

-Ray.