One Billion Pound Raffle Part 2
For those who haven't read One Billion Pound Raffle Part 1, then please do.
Alright,
from Part 1, we saw that for 50 people participating in the raffle with 50 marbles, 49 black and 1 red, each person had exactly 1/50 chance of winning the raffle.
From there, we can see that for n people participating in the raffle with n marbles, n-1 black and 1 red, each person had exactly 1/n chance of winning the raffle.
Now, your second challenge -
When the raffle rules are the same prove that when there's n people participating in the raffle, with n marbles, n-1 black and 1 red, and you are the k-th person in line, you have 1/n chance of winning the One Billion Pound Raffle.
***Alright, for those who thought you can actually look at the marbles when you are drawing one from the bag, you can't (and yes, I actually look at the replies)***
***Part 3 will be posted soon***
Alright,
from Part 1, we saw that for 50 people participating in the raffle with 50 marbles, 49 black and 1 red, each person had exactly 1/50 chance of winning the raffle.
From there, we can see that for n people participating in the raffle with n marbles, n-1 black and 1 red, each person had exactly 1/n chance of winning the raffle.
Now, your second challenge -
When the raffle rules are the same prove that when there's n people participating in the raffle, with n marbles, n-1 black and 1 red, and you are the k-th person in line, you have 1/n chance of winning the One Billion Pound Raffle.
***Alright, for those who thought you can actually look at the marbles when you are drawing one from the bag, you can't (and yes, I actually look at the replies)***
***Part 3 will be posted soon***
posted by James Yu at
2:01 PM
8 Comments:
First Post?
Why me?
I don't understand why this differs
from the first post except that instaed of being 1/50 chance here's there's 1/n chance.
The Kth person does not make a difference. One person draw one unknown marble. You run out of marbles at the end of the line.
I suppose you want a math equation to show the chance is 1/n.
Maybe someone else will see the Trick?
I can't see it. What's the "Trick"?
What if n = infinity?
n-1 Black marbles and 1 Red marble.
And my position in line,K is n/2.
Is my chance still 1/n ?
I would say my chance of winning is zero, because I would die of old age before my turn to draw came up.
I don't see how it differs from the first one easy, I was trying to find the trick also. I'll try explaining it like I did in part one using k instead.
Person who is K-th in line has a (n-(k-1))/n chance of drawing, and a 1/(n-(k-1)) chance of winning if he does draw. If you multiply those together the nominator and denominator cancel out and you are left with 1/n, regardless of what k is.
I think that is the proof he is looking for to show how it is 1/n regardless of what position.
theres no real question? >.> or am i just really that dense right now?
No, there is no real question. Though I can't say anything about the density...
He didn't use a question mark, but if you read the statement, he asks you to prove that the person who is k-th in line has a 1/n chance of drawing the ball. So that is the question. As far as your density goes.....
You are right. There was no question. Just a statement instructing you to "Prove " such and such.
Let's see the proof that there's a Billion Pounds for the winner first.
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