Impossible probability

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oemlegoem

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Here is the riddle. Anyone knows the solution and can explain why?

A teacher and his/her pupils are arranged along a circle. The teacher has a ball. He/she throws the ball with equal probability to the pupil to his/her left or right. The person who receives a ball also throws it with equal probability to the person on his left or right.

Which pupil has the highest probability to be the last one to receive the ball?
 
oemlegoem said:
Here is the riddle. Anyone knows the solution and can explain why?

A teacher and his/her pupils are arranged along a circle. The teacher has a ball. He/she throws the ball with equal probability to the pupil to his/her left or right. The person who receives a ball also throws it with equal probability to the person on his left or right.

Which pupil has the highest probability to be the last one to receive the ball?
Click to expand...
Can we call the first throw to be the last throw ? The question is kind of non-sense, as posted.

What do you think is the answer?

Why do you think that is the answer?
 
The ball game continues until there is only one pupil left who has not gotten the ball yet.

Someone told me all pupils have the same probability, which I have a hard time to believe. But I was told it is true. But how to explain it?
 
BigBeachBananas said:
You have to define how many throws can there be. The answer changes as the number of throws changes.
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I responded just before your post, and it was held for a while waiting for moderation.
The ball game continues until there is only one pupil left who has not gotten the ball yet. So there is no fixed number of throws. The number of throws could be infinite.
But apparently, all pupils have the same probability to be the last to catch the ball. But how to prove it?
 
oemlegoem said:
I responded just before your post, and it was held for a while waiting for moderation.
The ball game continues until there is only one pupil left who has not gotten the ball yet. So there is no fixed number of throws. The number of throws could be infinite.
But apparently, all pupils have the same probability to be the last to catch the ball. But how to prove it?
Click to expand...
math.stackexchange.com

What is the probability of being the last to touch an object passed around a circle of $N+1$ people?

We have $n+ 1$ people numbered by $0,1,...,n$ standing in a circle. Person $0$ has a bag of chips to start passing around. Every time, the person $k$ who is holding the bag of chips has probabili...
math.stackexchange.com math.stackexchange.com
 
I tried to calculate with excel. According to this, the pupils opposite to the teacher have the highest probability to catch the ball last. But that is different from the link that BigBeachBananas posted.
Where do I go wrong, or where does the link go wrong?
 

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It makes sense for your result to be the opposite because your scenario is strictly passing left or right. Since the pupil that is opposite of the teacher furthest away from the teacher, he/she will have the highest chance of touching it last. Whereas the scenario in the link I provided allow passing around the circle not constrained to the left or right aka a random walk around an n circle.
 
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BigBeachBananas said:
It makes sense for your result to be the opposite because your scenario is strictly passing left or right. Since the pupil that is opposite of the teacher furthest away from the teacher, he/she will have the highest chance of touching it last. Whereas the scenario in the link I provided allow passing around the circle not constrained to the left or right aka a random walk around an n circle.
Click to expand...
I was surprised by my simulation script which showed the probabilities being equal for all students. The script only allowed passing to the next left or right.
 
blamocur said:
I was surprised by my simulation script which showed the probabilities being equal for all students. The script only allowed passing to the next left or right.
Click to expand...
Yes, you're right, I made the mistake of thinking that once the teacher passed to the left, you can't give past the teacher to the right and vice versa. The probably should be relatively the same for everyone. Slightly different for n is even or odd.
 
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