Request to Improve the Complexity of a Probability Question for students

[zak100]

TL;DR Summary

Let’s suppose there are 3 persons and each one is rewarded a gift but when he sees the gift he has got two options, he can either accept the gift or reject the gift. What is the probability that a person can reject the gift?
Formula= number of successful outcomes/ Total number of equally likely outcomes
= 1/2

Hi,
I want to frame the above Probability question for computer science students. I have stated my idea above but I want to refine it so that it becomes a more comprehensive real world problem.

Zulfi.

 

[berkeman]

Let’s suppose there are 3 persons and each one is rewarded a gift but when he sees the gift he has got two options, he can either accept the gift or reject the gift. What is the probability that a person can reject the gift?

These seem like unrelated events so far, given your problem statement. What is the significance of there being 3 persons?

And who knows how the people will evaluate the gifts and decide whether to keep them or not?

Sorry, at least to me, the problem statement seems very underconstrained. How could anybody do a calculation based on this problem statement so far?

 

[zak100]

Hi,
Please give me some idea to modify it. I have to keep the gifts and the concept of acceptance/rejection. But I can't figure out to enhance the question.

One idea which just came into my mind is that they might be possessing the gift already or the gift requires some additional cost to carry. Some thing like that, can't figure out how to extend the problem beyond the initial question. Please guide me.

Zulfi

 

[berkeman]

Hi,
Please give me some idea to modify it. I have to keep the gifts and the concept of acceptance/rejection. But I can't figure out to enhance the question.

One idea which just came into my mind is that they might be possessing the gift already or the gift requires some additional cost to carry. Some thing like that, can't figure out how to extend the problem beyond the initial question. Please guide me.

Zulfi

https://en.wikipedia.org/wiki/Monty_Hall_problem

 

[FactChecker]

I think you have omitted some important parts of the problem statement. You say that each person can reject the gift and then ask for the probability that a person can reject the gift. I would say that the probability is 1.

 

[Mark44]

I think you have omitted some important parts of the problem statement. You say that each person can reject the gift and then ask for the probability that a person can reject the gift. I would say that the probability is 1.

Here's my best guess at what's happening here. Zulfi is tasked with creating a problem or modifying an existing problem. Zulfi is not a native speaker of English, so when he wrote "the probability that a person can reject a gift," I believe that he meant "the probability that a person rejects the gift."

The information that there are three people seems like a red herring, and not having at least an estimate for how often someone rejects a gift makes it impossible to answer the question.

 

[FactChecker]

Here's my best guess at what's happening here. Zulfi is tasked with creating a problem or modifying an existing problem. Zulfi is not a native speaker of English, so when he wrote "the probability that a person can reject a gift," I believe that he meant "the probability that a person rejects the gift."

That sounds right.

The information that there are three people seems like a red herring, and not having at least an estimate for how often someone rejects a gift makes it impossible to answer the question.

If the goal is to formulate a problem, then that may be something that can be added/changed to make a better problem. The OP is not asking for a calculated answer.

 

[Klystron]

Consider a pool of gifts. Each guest brings one gift of ~equal value to the pool. The hostess assigns a number 1-N to each gift then places a copy of each number in a vase. Each guest chooses a number.

The hostess calls each number in order. Each guest can accept the numbered gift or exchange theirs with a gift already chosen (but may not take higher numbers). This game is common at Xmas parties.

Now the teacher can assign a few given odds and formulate many questions such as:

• What is probability (P) of guest [1-N] choosing their own gift?
• If guests keep original gift half the time, what is P that first guest #1 keeps first choice?
• Guest #2? etc.
• How many times can gift #1 change hands?
• Gift number integer(N/2)? etc.

Let guests choose in pairs (couples) if you prefer. Follow gifts or guests in formulating questions. Variant: allow guests to exchange numbers after drawing. Who has best choice of gift?

 

[zak100]

Hi,

Thanks Klystron for providing this great improvement.

Thanks everybody who replied.

I have got some clue. I would work on that. Problem not completely solved but I have good material to improve on.

Zulfi.

 

[Klystron]

Hi @zak100, you may be interested in reading this thread on assigning housing to agents. If you translate house = gift and agent = guest and assign utility values, the computations may be relevant to your treatment.

I am reading the cited research paper: http://cramton.umd.edu/market-design/abdulkadiroglu-sonmez-house-allocation.pdf and studying the replies. Good luck.

 

[zak100]

Hi,

Both the threads are posted by myself. Is there any way to convert the problem into Np hard problem?
Zulfi.