Chance/probability question

[Wits' End]

My son and I were talking about this subject the other day and I couldn't answer w/ enough confidence to convince him (or me). Any help for the correct answer would be welcome.

You have a container with 9 orange balls and 1 white ball. Assume that people drawing balls have no way of knowing what they have untill after all are drawn. You have 10 people drawing out the balls. Is there a diiference between the odds of a specific person getting the white ball, Drawing them all at once or drawing them one after the other?
I know this isn't quite clear but I think those who are interested will get it, even if you understand it slightly differently than I your anwer will probably help.
I won't be back till Monday AM. Central

 

[txwest]

The odds are the same. It's not the drawing that sets the odds, it's the displaying. If you drew one at a time, but didn't display what you drew until everyone was finished, your odds of having the white ball are the same. 9 out of the 10 people have a 100% chance of having an orange ball. 1 person has a 100% chance of getting the white ball. If you are drawing & displaying at the end of each draw, overall you'ld have a 1 in 10 chance. But the odds would change at the beginning of each draw, since the # of orange balls would decrease at each drawing. All depends on if you figure the overall or individual odds. TX

 

[Lux Luthor]

[No message]

 

[Max]

If you all grab a ball at the same time or one after the other, there is no difference as long as nobody can see what anybody picked until all the balls are chosen.

For example, if I can see what ball the first person draws, then that changes the odds for the remaining 9. If the first person draws a white, then I know everybody's chances of drawing a white are 0. If the first person draws an orange, then everybody's odds changes to 1 in 9 white instead of 1 in 10.

The point is that it is only the new information that changes the odds because that changes the game. If this game were to be repeated over and over again, the odds of getting the white ball are 10% no matter if you go first, last or 7th.

 

[Tater Rocket]

That isn't strictly true. If the first person draws a white and everybody sees it, he puts it back and everybody still has a 1 in 10 chance of drawing a white.

What my prob and stats teacher called it is "Drawing with replacement" (then everybody's odds are the same) and drawing without replacement (then they are not). Oh, and max is right on that part, this would only hold true for one game, if you kept repeating it everybody's chance would be 1 in 10.

Spud

 

[rrtanton]

This all reminds me of how confusing probability can be! It depends a great deal on how you think about a situation, and you can catch yourself making assumptions that you didn't even know you were making. Here's an example used often by professors, the "Monty Hall" problem (this is a fun one...):

You're a contestant on "Let's Make a Deal." Monty Hall shows you three doors and tells you that behind one of them is a new car, and behind each of the other two is a goat. You get to pick a door and win whatever's behind it. So, you choose a door (let's say it's #1), but in typical Monty style, he says "Now before we open your door, let's see what was behind door #3!" He opens door #3 and reveals a goat. Monty then asks you if you'd like to change your mind and choose door #2. Should you?

rusty

 

[Jonathan]

Well now you've gone and done it. No discussion of flashlights for at least the next three weeks

 

[star882]

"You're a contestant on "Let's Make a Deal." Monty Hall shows you three doors and tells you that behind one of them is a new car, and behind each of the other two is a goat. You get to pick a door and win whatever's behind it. So, you choose a door (let's say it's #1), but in typical Monty style, he says "Now before we open your door, let's see what was behind door #3!" He opens door #3 and reveals a goat. Monty then asks you if you'd like to change your mind and choose door #2. Should you?
If you want to.
You already know that #3 is a goat, so #1 and #2 have an equal chance of having a car.

 

[Max]

Originally posted by Tater Rocket:
What my prob and stats teacher called it is "Drawing with replacement" (then everybody's odds are the same) and drawing without replacement (then they are not). Oh, and max is right on that part, this would only hold true for one game, if you kept repeating it everybody's chance would be 1 in 10.

Spud

<font size="2" face="Verdana, Arial">Drawing without replacement still doesn't change the 1 in 10 probability for each person if you assume that nobody can see what balls have been drawn until the end. What drawing without replacement does do is change the number of possible outcomes. For example, with replacement, the chance that nobody picks the white ball is around 35%, whereas without replacement that outcome is impossible.

 

[Max]

Originally posted by star882:

You already know that #3 is a goat, so #1 and #2 have an equal chance of having a car.

<font size="2" face="Verdana, Arial">Oh, but that's the trick! They don't have an equal chance.

 

[Lux Luthor]

It wasn't exactly clear to me what the question was, so I deleted my original reply. But whatever it was, a simple way to determine probabilites is to make a chart containing all the possible outcomes.

This would be too much work for 9 orange balls, so I would use 2 of them instead, and 1 white ball.

 

[Alchemist]

Originally posted by rrtanton:


You're a contestant on "Let's Make a Deal." Monty Hall shows you three doors and tells you that behind one of them is a new car, and behind each of the other two is a goat. You get to pick a door and win whatever's behind it. So, you choose a door (let's say it's #1), but in typical Monty style, he says "Now before we open your door, let's see what was behind door #3!" He opens door #3 and reveals a goat. Monty then asks you if you'd like to change your mind and choose door #2. Should you?

rusty

<font size="2" face="Verdana, Arial">that sounds familiar. why not just ask Marilyn

 

[Tomas]

... and the cat in the box is neither dead nor alive ...

 

[rrtanton]

Cool! There's even a simulation...

Yes, that covers it quite well. Monty has been interviewed about this, and has spoiled our fun a little by saying that, were this the real deal, he'd remember the statistics and manipulate the situation to keep the contestant's odds uncertain...such as, perhaps only showing a goat if he knows the contestant has chosen the car.

And yes, the cat is neither dead nor alive, but although I understand the concept behind why, I can't explain it very well. I LOVE stuff like that!

 

[Wits' End]

Thanks for the replies--