Statistics and probability

[Sparrisen]

I just wanted to share with you my love for this. I have in my life understood this completely about 4 times, most recently in the university, but every time I want to use it again, I seem to have forgotten even the most fundamental behaviours.

I will want to keep this thread for future use, since I will now post some questions, and hope that someone more mathematically gifted than me can answer:

Lo and behold, you have bucket filled with 20 balls. 19 are white, one are brown. You pick up a ball, look at the colour, and put it back again, and repeat this procedure 10 times. What are the chance that you get the brown ball AT LEAST once?

How about twice?

By digging into my mind, I have brought out the following formula: the probability= a/b, where a is instances with a brown ball, and b are the total number of instances.

[Brummy]

i dont that it is right but i would say this:
first:

10 / 20 = 0.5
first is 50%

second:

10 / 20 / 2 = 0.25
second is 25%


but im not sure ...

[Oynamak]

hm.. 5% each time, so .. 5x10x5/3 .. = 83.3% .. thats right?? lol. I've got no idea :p

[Nightmare]

I studied probabilities quite a lot once, but unfortunately that's like 5-6 years ago, so don't remember much anymore... I probably have the books somewhere still so could look up the solution, but let's see if someone makes it before me

[Brummy]

chances each time: 1:20.  If you take a ball and put it back, there are still 20 balls, 19 white, 1 brown. So if you take another one, you've got the same chance as before. Nothing chances, your chances won't get bether/worser imo. so its always 1:20, means 5% to get the brown ball each time you take a new one, even the 10th try wont give you more than 5% chance to get the brown one (:


am I right?


1/20 =0.05 .. 0.05 = 5%. then you have 19 balls, but you put it back, means, if you take a new ball you've got again : 1/20.. thats 0.05, and thats 5% again.. 3rd try = same chance.. and so on..

u have 10 tries so the 5% * 10

[Oynamak]

u have 10 tries so the 5% * 10

5% 10 times = 5*10 seems to easy to me. imo he wouldnt ask this question if the answer is that easy :p  imo its smth around 50-99% ^^ ... but 5%*10 sounds like a consequentially answer :p

[SirTeoHero]

If you wouldn't put that ball back, then it would be 50%. But now its 1/20 everytime, since you can end up picking same ball over and over again. And if you star placing balls to that bucket, its not about propablity. So 1/20^10

[Nightmare]

It's not 0.05*10 because that would mean your chances would exceed 100% at some point, which ofc can't be possible.

Also it's not 0.05^10 because that just decreases your chances with every attempt, which is also is not possible.


Unfortunately I don't have the correct answer yet, but atleast I know those which are not correct

[Smiskfisk]

Ok, my answer is 40.13%

[mayhem]

Fish is right

40,126306%

[SirTeoHero]

Well ok, my answer was incorrect, but how could chances increase after picking ball? Since the same ball goes back and you you have totally same changes again, just like before the first ball, since that ball what you picked can't help you on anyway. You can't know where you placed it so its as random as it was before. So here is my new answer: 0,05, it doesn't change.

[Brummy]

he didnt ask "How high are the chances to get the brown ball if u took 10 times a ball out and put it back".
He asked "How high are the chances that u get the brown ball once if u have 10 tries to get it."
at least as far as i understood.


And if u say "its allways 5%" then ure totally wrong. 19 white 1 brown ball. U have 100.000 ties and if u try it out u wont get the brown ball only with every 2.000.000 try

[Gleipdonir]

ahhh. i've got a nice one of that too:
(Taken from a game-show)

There are 3 doors. Behind one of them there is a car, behind the other two a goat.

Now, lets say someone (the player) elects door 1. The game host then opens door 3 to reveal a goat and offers to let the player pick door 2 instead of door 1. (After the player picked up a door, the game host always opens a door which reveals a goat!)

And now the ultimate question: should the player change to door 2 or not.

(Yes, no, maybe, doesnt matter?)

[mayhem]

He should (yes I am too lazy to explain my answers )

[SirTeoHero]

Brummy, didn't get you.
Tell me, why would chances be better after the first ball?. This same can be done with 20 different buckets, every bucket has 19 whites and one brown. First try is on bucket 1, chances are 1/20. No luck, then you go to bucket 2, what are the chances there? Same as before. The probablitity can't chance if nothing else chances, or if it would then on bucket 20, you would have 100% chance to get that ball, but it isn't like that.