Friday Homework 3

A

AnthonyGerrard

Registered User.
Local time
Today, 01:29
Joined
Jun 11, 2004
Messages
1,069
This has been asked here before, it the perfect follow up to last weeks.
**Its just a bit of fun**!

It will no doubt be controversial, it always is - but only to those who haven't actually understood it yet. Its caught me out before.

----------------

Imagine a gameshow similar to deal or no deal - there are three boxes with £1, £2 and £1,000,000 in them.

The host knows whats in all the boxes, the contestant knows nothing of which box the various prizes are in. (he knows the value of the prizes)

The contestant must pick a box . The host must then open one of the remaining 2 boxes to reveal one of the lesser prizes.

The show always by design finishes with 2 boxes unopen, one with the host, one with the contestant (the box the contestant picked for themselves). One of the remaining 2 boxes must have the jackpot in. (the host by the rules of the show - must only reveal a box that does not have the jackpot in and that box must be one of those not chosen by the contestant, and must do this every show as the rules of the show)

So given theres now just 2 boxes left - Whats are the odds the contestant has the box with the jackpot? Should he switch if offered the chance?


------

Hint - think about the show with 30 boxes (one with 1,000,000 and 29 with less than 30 quid each in) and run through the show in your mind, contestant picks one, host opens 28 others revealing small prizes , necesarily by the rules of the show leaving the jackpot in one of the two remaining boxes. Whats are the odds the contestant has the box with the jackpot? Should he switch if offered the chance?

:-)
 
I remember that this caused an argument, sorry discussion, last time it was on here. Not sure if its worded exactly the same as it is cleat that the odds are evens given that we are told that there are 2 boxes one with the jackpot.

Brian
 
Brianwarnock said:
I remember that this caused an argument, sorry discussion, last time it was on here. Not sure if its worded exactly the same as it is cleat that the odds are evens given that we are told that there are 2 boxes one with the jackpot.

Brian
Click to expand...

Did you try the hint?
 
I read it all , but I still stand by the final fact that there are two boxes one containing the jackpot and one not, what happened before is irrelevant to the odds on the final choice.
People divided into two camps last time, maybe they will again, but I will not be persuaded to change. :D

Brian
 
Whats are the odds the contestant has the box with the jackpot?

Answer 1 in 3


Should he switch if offered the chance?

Answer Yes
 
The Monty Hall problem!

But the inconvenient truth here is that it's not 50-50 - in fact, switching doubles your chances of winning.
Click to expand...
 
Correct! 1/3 and 1/30 for the hint.

For a bonus point - explain why its not 50/50!

Or why for this example - are the odds (for the box chosen by the contestant) the same after the reveals, whereas in last weeks the odds are changed after the test?!
 
The catch is that the Host is not making a random selection.

This should change how you look at the problem.
 
If I wasn't in such good company as mentioned in the link I would begin to think that I am thick, which may still of course be true, however surely in the last instance the contestant has a choice of two boxes, therefore it is a 50-50 chance.

I notice that the guy only did the test once and the result was not double for the switchers.

As I said , I don't get it, but may have to live with that.

Brian
 
Brianwarnock said:
If I wasn't in such good company as mentioned in the link I would begin to think that I am thick, which may still of course be true, however surely in the last instance the contestant has a choice of two boxes, therefore it is a 50-50 chance.

I notice that the guy only did the test once and the result was not double for the switchers.

As I said , I don't get it, but may have to live with that.

Brian
Click to expand...

The result is near enough double for the swtichers!
 
I will try to explain as simply as possible.

We have boxes "A", "B" and "C".

The prize is in one box.

Select any box and the odds are 1 in 3 that you have chosen the prize.

This does not matter if the box chosen is "A", "B" or "C".

Assume you chose "A" with odds of 1 in 3, then if another person joined the game and was given both "B" and "C". The second person would have a 2 in 3 chance of winning the prize.

Now let us make it easier for the second person by removing a box that is not the prize. The odds for the second person has not changed at 2 in 3 because they were always allowed two choices. All that has happened is one of their boxes was removed but not the box with the Prize.

Worth repeating.

So the second person's odds have not changed at 2 in 3 it is just that one wrong answer has been removed.

Your original choice has not changed at 1 in 3 for box "A".

If you changed your choice to the two boxes with one incorrect box removed then you would now have a 2 in 3 chance of winning.


Now a different way to look at it.

The odds of winning if you chose one box is 33%.

The odds of winning if you chose two boxes is 66%.

The rest of the information you have been given is just to cloud the issue so that you look at the wrong thing.
 
Last edited:
I remember posting this years back. It caused quite a debate.
 
AccessBlaster said:
It's like roulette, people will bet black or red thinking they have a 50/50 chance. But they miss the zero or in some cases double zero which are green. One green in a sea of black and red tilts the odds in favor of the house.

The real paradox comes when you realize the tax bill that comes with your free gift. Nothing free, except the cheese in the trap!
Click to expand...

In Australia you do not pay tax on your winnings.

If they did tax winnings then they would have to allow deductions for losses.

Only declared professionals pay tax.
 
RainLover said:
The problem is that they go broke trying to win.

Especially "Poker Machines".
Click to expand...

Is that why they are called Pokies?

The pokies room of Aussie pubs, really is the land of the living dead.

One of the few things in terms of regulation that Australia seems backward upon, is gambling, actually maybe it is further advanced down the road to hell, and we seem to be following down the same terrible road with fixed odds machines.
 
You must log in or register to reply here.

Similar threads

Uncle Gizmo
Microsoft’s “Premier” Mix-Up: A Tale of Access and Amnesia
Replies
1
Views
354
Isaac
Isaac
S
IIF with 2 conditions
2
Replies
20
Views
581
Mark_
M
Steve R.
Democrats Continue to Obstruct Election Integrity
2
Replies
27
Views
970
Isaac
Isaac
J
Why
2
Replies
25
Views
819
AccessBlaster
A
J
One last time
2
Replies
29
Views
704
ColinEssex
ColinEssex

Users who are viewing this thread

Total: 1 (members: 0, guests: 1)
Back
Top Bottom