1. ## Balls!

Jezza da Vinci was a courtier to King Ursus. King Ursus was desperate to marry off his son, Arctos, to the daughter of King Kodiak, Bruin.

Now it appears that King Kodiak had a very cunning way to sift out the many suitors who asked for the hand of Bruin. King Kodiak would place two identical vases on a table in front of his throne and then hand the suitor, 100 black balls and 100 white balls (all exactly the same size and weight). He would then ask the suitor to put all the balls into the vases, in any combination they wanted. Once done he would ask Bruin to enter the room and pull out a ball from one of the vases. If the ball was black then the suitor whould be allowed to marry Bruin.

Arctos was confused and confounded by this puzzle, what could he do to get the beautiful Bruin to select a black ball? He turned to Jezza da Vinci for help.

Jezza da Vinci turned to Arctos and said " That's easy, I can't make her choose a black ball, but I can improve your chances that she will! Here I'll show you"

How did Jezza da Vinci split up the balls improve Arctos's chances?

2. ## Re: Balls!

Assuming that the balls are going to be thoroughly stirred before she chooses, the best I can do is
Vase 1: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> 1 Black ball, no white balls</span hide>
Vase 2: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> 99 Black balls, 100 white balls</span hide>

This gives odds of <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">(1 + 99/199) /2 = </span hide>74.87%

StuartR

3. ## Re: Balls!

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Put one black ball in the first vase, and all 199 remaining balls in the other one. If Bruin selects a vase at random and draws a ball from it at random, the probability of drawing a black ball is 1/2*1 + 1/2*99/199 = 0.7487... or almost 75%.</span hide>

4. ## Re: Balls!

Hi Stuart/Hans

Appears this was a test of speed typing as you both leapt on it at the same time <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

You both get a [choccy bar] but Stuart gets a tin of [lemony sherbert travelling sweets] for being fastest

5. ## Re: Balls!

Oh good, I was dreading some savoury <img src=/w3timages/censored.gif alt=censored border=0> that I wouldn't want to eat. I love those [lemony sherbert travelling sweets]. Can I have the [choccy bar] before I go to bed tonight please.

6. ## Re: Balls!

Of course, but make sure you clean your teeth afterwards <img src=/S/blackteeth.gif border=0 alt=blackteeth width=20 height=20>

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