permutations/combinations question

[mountainboii]

I always enjoyed things like this too.  Derren Brown talks alot about this sort of thing in one of his books and its quite interesting.  The one I used to like to use with people was the three door prize.  Say you are on a game show and at the end you get to choose from three doors to win a prize.  Behind one door is the prize.  Behind the other doors are booby prizes.  You pick a door, the game show host then opens one of the other doors to reveal a booby prize.  The host then asks you would you like to change your door.  Should you change?  This appeared in 21 there last year

I hate that one. One of my flatmates last year was doing a Maths PhD and I remember him trying to explain how this works to me. Still none the wiser 

[magickingdom]

I always enjoyed things like this too.  Derren Brown talks alot about this sort of thing in one of his books and its quite interesting.  The one I used to like to use with people was the three door prize.  Say you are on a game show and at the end you get to choose from three doors to win a prize.  Behind one door is the prize.  Behind the other doors are booby prizes.  You pick a door, the game show host then opens one of the other doors to reveal a booby prize.  The host then asks you would you like to change your door.  Should you change?  This appeared in 21 there last year

it doesnt matter whether you change your door its 50:50 at that stage

[Puckoon]

I always enjoyed things like this too.  Derren Brown talks alot about this sort of thing in one of his books and its quite interesting.  The one I used to like to use with people was the three door prize.  Say you are on a game show and at the end you get to choose from three doors to win a prize.  Behind one door is the prize.  Behind the other doors are booby prizes.  You pick a door, the game show host then opens one of the other doors to reveal a booby prize.  The host then asks you would you like to change your door.  Should you change?  This appeared in 21 there last year

it doesnt matter whether you change your door its 50:50 at that stage

Not right, the odds have changed from 1/3 to 2/3 in your favour.

I cheated.

[mountainboii]

I always enjoyed things like this too.  Derren Brown talks alot about this sort of thing in one of his books and its quite interesting.  The one I used to like to use with people was the three door prize.  Say you are on a game show and at the end you get to choose from three doors to win a prize.  Behind one door is the prize.  Behind the other doors are booby prizes.  You pick a door, the game show host then opens one of the other doors to reveal a booby prize.  The host then asks you would you like to change your door.  Should you change?  This appeared in 21 there last year

it doesnt matter whether you change your door its 50:50 at that stage

Apparently not, it took me ages to get my head around it but you have a 2/3 chance if you switch.

This helped:

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

[Bogball XV]

Not sure about Russia but in countries like India and China the male to female live birth ratio (6:5) is much more skewed towards male children.  More to do with aborting female children than anything evolutionary.

I don't know, but I'd be shocked if abortions were the reason for this - despite the recent economic advances in both countries in recent years I can't see that a remotely significant proportion of expectant parents would be in a position to know the sex prior to birth.

[muppet]

Brilliant puzzle that.

Best explanation I read was this one:

It may be easier to appreciate the solution by considering the same problem with 1,000,000 doors instead of just three (vos Savant 1990). In this case there are 999,999 doors with goats behind them and one door with a prize. The player picks a door. The game host then opens 999,998 of the other doors revealing 999,998 goats—imagine the host starting with the first door and going down a line of 1,000,000 doors, opening each one, skipping over only the player's door and one other door. The host then offers the player the chance to switch to the only other unopened door. On average, in 999,999 out of 1,000,000 times the other door will contain the prize, as 999,999 out of 1,000,000 times the player first picked a door with a goat. A rational player should switch. Intuitively speaking, the player should ask how likely is it, that given a million doors, he or she managed to pick the right one

[mountainboii]

Not sure about Russia but in countries like India and China the male to female live birth ratio (6:5) is much more skewed towards male children.  More to do with aborting female children than anything evolutionary.

I don't know, but I'd be shocked if abortions were the reason for this - despite the recent economic advances in both countries in recent years I can't see that a remotely significant proportion of expectant parents would be in a position to know the sex prior to birth.

Post-natal 'abortions' perhaps 

[The Watcher Pat]

Not sure about Russia but in countries like India and China the male to female live birth ratio (6:5) is much more skewed towards male children.  More to do with aborting female children than anything evolutionary.

I don't know, but I'd be shocked if abortions were the reason for this - despite the recent economic advances in both countries in recent years I can't see that a remotely significant proportion of expectant parents would be in a position to know the sex prior to birth.

Post-natal 'abortions' perhaps 

China had a one child policy for ages...Think they still might have...Lots of female children were aborted as couples wanted males to carry on the family name ...so to speak...



http://en.wikipedia.org/wiki/One-child_policy

[magickingdom]

I always enjoyed things like this too.  Derren Brown talks alot about this sort of thing in one of his books and its quite interesting.  The one I used to like to use with people was the three door prize.  Say you are on a game show and at the end you get to choose from three doors to win a prize.  Behind one door is the prize.  Behind the other doors are booby prizes.  You pick a door, the game show host then opens one of the other doors to reveal a booby prize.  The host then asks you would you like to change your door.  Should you change?  This appeared in 21 there last year

it doesnt matter whether you change your door its 50:50 at that stage

Apparently not, it took me ages to get my head around it but you have a 2/3 chance if you switch.

This helped:

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

i'm with the people who cant get that. if you choose your door from 3 and AFTER you choose you door the host opens a dud one i cannot possibly see how your chances improve if you change doors. the fact is your left with 2 doors one a dud one not 50:50

[Hound]

i'm with the people who cant get that. if you choose your door from 3 and AFTER you choose you door the host opens a dud one i cannot possibly see how your chances improve if you change doors. the fact is your left with 2 doors one a dud one not 50:50

Its a good one alright.

Maybe it could be explained like this.

You've three doors to pick from to win the big prize. You choose A.

Then before any doors are opened, you are given the choice to change to BOTH B and C.  So by sticking with A, you'd have a 1/3 chance of winning but by choosing B and C, you have 2/3 chance of winning. So given the choice any logical person would choose B and C to give themselves the 67% chance, rather than stick with A and 33%.

Now you know that one of B and C contains the booby prize. At least one of them must have a booby prize.

So the host shows you that B has a booby prize. Does that mean your chances of winning have reduced from 67% to 50%?? Even though you knew before B was opened that one of your doors had the booby prize?

[muppet]

i'm with the people who cant get that. if you choose your door from 3 and AFTER you choose you door the host opens a dud one i cannot possibly see how your chances improve if you change doors. the fact is your left with 2 doors one a dud one not 50:50

Its a good one alright.

Maybe it could be explained like this.

You've three doors to pick from to win the big prize. You choose A.

Then before any doors are opened, you are given the choice to change to BOTH B and C.  So by sticking with A, you'd have a 1/3 chance of winning but by choosing B and C, you have 2/3 chance of winning. So given the choice any logical person would choose B and C to give themselves the 67% chance, rather than stick with A and 33%.

Now you know that one of B and C contains the booby prize. At least one of them must have a booby prize.

So the host shows you that B has a booby prize. Does that mean your chances of winning have reduced from 67% to 50%?? Even though you knew before B was opened that one of your doors had the booby prize?

I liked the explanation I posted above but that is a very good one as well Hound.

[mountainboii]

Being explained on Horizon on BBC2 right now