Maths / Probability Puzzle

[Kellfire]

You're over thinking it. You just aren't getting the maths.

 

[TheDiablo]

Seriously!?

There's a 50% chance you have made the right choice. Makes no difference if you swop, you still have a 50:50 chance of being right.

That is so obvious I can't believe anyone can think otherwise.

Get it yet? 😂😂😂

Muppet.

 

[Hacker Khan]

Maybe I am missing something but he says that one of the doors has a booby prize behind it - it doesn't mean that both don't

So both the other two doors you haven't chosen could have a booby prize

2 doors have a booby prize, one door has the car. After your first guess you get shown one of the other doors you have not chosen has a booby prize. That is when your odds are no longer 1 in 3.

 

[jim8flog]

This is about knowing the difference between odds and probability.

Tossing a coin will always have the same odds of it being either heads or tails but the more you toss the coin with the same result the greater the probability that the next toss will produce a different one. Probability is a statistical concept, odds are a mathematical concept.

 

[Jimaroid]

In the last 20 years I have seen this puzzle posted to numerous usenet newsgroups, bulletin boards, forums, social media groups, mailing lists and even discussed openly in pubs and clubs . It has never resulted in anything except a massive argument.

My prediction, 100% probability of the same thing happening again here.

 

[gmhubble]

2 doors have a booby prize, one door has the car. After your first guess you get shown one of the other doors you have not chosen has a booby prize. That is when your odds are no longer 1 in 3.

Why do your odds change as you still don't know which one of the other two doors has the booby prize behind it

 

[Papas1982]

Why do your odds change as you still don't know which one of the other two doors has the booby prize behind it

Having looked at a link earlier. The easiest way I can explain it is:

from the start you have 1/3 of picking it at the start. Meaning 2/3 of not.

He then removes a bogus box. Meaning that the left box has a 2/3 chance of being the right one.

so you stick with your box 1/3 or go with the switch 2/3.

 

[gmhubble]

Having looked at a link earlier. The easiest way I can explain it is:

from the start you have 1/3 of picking it at the start. Meaning 2/3 of not.

He then removes a bogus box. Meaning that the left box has a 2/3 chance of being the right one.

so you stick with your box 1/3 or go with the switch 2/3.

He doesnt remove anything .... he just says that behind one of the doors is a booby prize .... it also does not mean that there isnt a booby prize behind the other one either!!!!

 

[Papas1982]

He doesnt remove anything .... he just says that behind one of the doors is a booby prize .... it also does not mean that there isnt a booby prize behind the other one either!!!!

He is given 3 choices at the start. So has 1 in 3 it'll be in his box. (A)

Therefore its 2/3 it'll be in one of the two he doesn't pick. (B)

The full description then then states that he removes a box, one that doesn't have the prize in. The contestant can Then swap.

If you accept that (a) is true, then option (b) remains 2/3 irrespective of there now being one box instead of two.

 

[Maninblack4612]

Get it yet? 

Muppet.

It's reassuring to know that a professor of mathematics got it as wrong as me. The way I explain it to myself is that, at the outset, I'm twice as likely to have chosen the wrong door. When one wrong door is opened this is still the case so, by switching, I double my chances of choosing the right one. Defies logic!

 

[SwingsitlikeHogan]

Was not a great fan of stats when doing my degree - ended up using them every day for 10 years n my first job.

But I did like the statistical 'fact' that you only need 23 people selected at random from the population for there to be a 50% chance that two of the selection will have the same birthday.

Note that this doesn't mean that if you have 56 people split randomly into two groups there is 100% probability that two people in one of the groups will have the same birthday - but that's stats for you.

 

[larmen]

He doesnt remove anything .... he just says that behind one of the doors is a booby prize .... it also does not mean that there isnt a booby prize behind the other one either!!!!

It's about likelihood, not certainty.

Personally, I would go for doubling the chance. But also, I am 'unlikely' to attend a silly gameshow in the 1st place.

 

[Foxholer]

Was not a great fan of stats when doing my degree - ended up using them every day for 10 years n my first job.

But I did like the statistical 'fact' that you only need 23 people selected at random from the population for there to be a 50% chance that two of the selection will have the same birthday.

Note that this doesn't mean that if you have 56 people split randomly into two groups there is 100% probability that two people in one of the groups will have the same birthday - but that's stats for you.

That was also one of our early introductory Stats 'stats'!
Using your numbers..... (364/365)**23 < 0.50 then!

 

[Pro Zach]

This is about knowing the difference between odds and probability.

Tossing a coin will always have the same odds of it being either heads or tails but the more you toss the coin with the same result the greater the probability that the next toss will produce a different one. Probability is a statistical concept, odds are a mathematical concept.

What you describe is wrong and is a logical fallacy often called the gamblers fallacy.

Odds and probability both mean the same thing - how likely something is. They only differ by describing likeliness in different contexts.

As you state, tossing a coin will ALWAYS have the same odds of being heads or tails. If heads comes up 5 times then the odds of a head or a tail on the 6th throw remains the same – because it ALWAYS has the same odds. It therefore cannot be more probable to produce a different one.

 

[Deleted member 15717]

As already posted....but

[video=youtube;Zr_xWfThjJ0]https://www.youtube.com/watch?v=Zr_xWfThjJ0[/video]

Switch and thanks for the extra %% of winning

 

[Tashyboy]

Phone a friend

 

[Foxholer]

This is about knowing the difference between odds and probability.

Tossing a coin will always have the same odds of it being either heads or tails but the more you toss the coin with the same result the greater the probability that the next toss will produce a different one. Probability is a statistical concept, odds are a mathematical concept.

Utter tosh!

 

[Hacker Khan]

This is about knowing the difference between odds and probability.

Tossing a coin will always have the same odds of it being either heads or tails but the more you toss the coin with the same result the greater the probability that the next toss will produce a different one. Probability is a statistical concept, odds are a mathematical concept.

I bet casino's love you....

 

[Region3]

I'm not sure what is sadder; the fact that people get insulted on here when they don't understand something, or that when it happens I'm not surprised any more.

 

[Slime]

Was not a great fan of stats when doing my degree - ended up using them every day for 10 years n my first job.

But I did like the statistical 'fact' that you only need 23 people selected at random from the population for there to be a 50% chance that two of the selection will have the same birthday.

Note that this doesn't mean that if you have 56 people split randomly into two groups there is 100% probability that two people in one of the groups will have the same birthday - but that's stats for you.

I'm no mathematician, but did you not mean 46 people split randomly into two groups?
i.e. 2 X 23 from your first fact.