## View Poll Results: Do you think the player should switch?

Voters
48. You may not vote on this poll
• Yes

20 41.67%
• No

13 27.08%
• Don't know

4 8.33%
• No difference

11 22.92%

# Thread: Problem on Mathematics - Probability

1. ## Re: Problem on Mathematics - Probability

Well... What's the probabilty that the host will want to open the other door for you to see? The host knows the location of the prize. If you have choosen the correct door, there is a higher probability that the host will attempt to confuse you. Most likely the case that he wants you to get the wrong door. Then the more you shouldn't change...

If you have chosen the wrong door, there's no need for the host to try so hard because he can easily save the prize from being given out unless he really wants to give out the prize so much...

Just imagine you're the one giving the prize... what will you do?

2. ## Re: Problem on Mathematics - Probability

Originally Posted by roygoh
The original situation is the same as if the guest were allowed to pick one box and then the host asked him if he/she would like to trade his/her one box for the BOTH the 2 boxes that he/she did not pick.
Exchange one unopen box for 2 unopen boxes is different from exchange one unopen box for one opened and one unopen boxes, furthermore, the opened box is for sure empty.

If the exchange activities may or may not happen, then better don't change if the host know which box contains the prize, this is a mind game.

Each one of us has a way to assume certain conditions, if the assumption is right, then the answer is right and wrong if assumption is wrong. The question is which should be the correct assumption which is where the debate never end. That is why I mentioned use a practical experiment to confirm the answer rather than assumption. It is not very difficult nor time consuming to proof it.

3. ## Re: Problem on Mathematics - Probability

Let's take another spin on this:

Let's say I run a game show. My show always ends with the player having to choose between two boxes, one of which contains a prize and the other nothing.

Then I get feedback that the viewers feel it's kinda boring, or maybe the sponsors and management wants more entertainment factor.

OK, so to spice up my show, I throw in one more box to make it look more difficult - three boxes to choose from - and then get the presenter to open one box but with lots of fanfare and suspense to captivate the audience and drive show ratings higher.

But, to me and the sponsors of the show, the amount of money written off for the program is still the same, but we get more bang for the buck as the show now attracts more attention, audience, but yet the probability of losing the main prize (and having to pump in more money to replace it for the next show) is still the same. Probability can be the same if we get the presenter to always open the empty box, or based on past historical data (ie. more losers than winners in the past), open the winning box to give the contestant and audience a happy ending.

4. ## Re: Problem on Mathematics - Probability

Originally Posted by hong2
Hi Roy,
this is really quite interesting. To switch or not to switch and the final answer is
YES and NO depending on the assumption:

1) YES (probability 1/3 and 2/3) if the host knows where the prize is, and your reasoning is correct.
2) NO (probability 1/2 and 1/2) when the host just makes a random pick, and my reasoning is correct.

Since your assumption is that the host KNOWS, then you are correct with your argument.

Since the host knows, this is not really a probability problem (randomness) anymore. One can argue that because of the your reasoning, the host will open an empty box to tempt the player to switch. Again it is assumed that the host was instructed to help keep the prize. Of course he could just be trying to make the show interesting. Good job though.

I have a similar problem. With a population of families with 2 children, given that one of the children is a girl, what is the probability that the other is also a girl? Seems quite simple? Have fun !
Just reviving an unanswered question to the OP, which is congruent with my thoughts on this. Did the host knowingly or unknowingly open the empty box? If the host had randomly picked one of the 2 remaining boxes and it turned out to be empty, nothing has changed, has it? As per the current "Deal or No Deal" rave, knowing the "hole" makes all the difference.

5. ## Re: Problem on Mathematics - Probability

The correct decision is to switch. Classic monty hall problem.

6. ## Re: Problem on Mathematics - Probability

yeah.
it's the same as "I give you 100 doors and you pick the door which you think contains the prize. Then I reveal to you that behind 98 doors are sheeps. Would you change or still keep to your choice?"
Read this from My Brain Is Open.

7. ## Re: Problem on Mathematics - Probability

if you consider that there are 2 stage of decision making.

1. you have 1/3 chance of picking it. Later on , you have 1/2 chance of still picking it. 1/2*1/3 = 1/6
2. you have 2/3 chance of not picking it. Later on you have 1/2 chance of not picking it. 2/3*1/2=1/3

IF on the other hand, you only have one decision making process.
your overall chance is always and always 1/3
So it's all in the mind. If contestant has decided only on 1 decision making process, it's probably the best choice.
So

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