Math people, solve this argument for me

[Erzengel]

I can hold my head a little higher tonight.

 

[The Squirrel]

Huzzah! Victory!

 

[wiegeabo]

Aw screw it. I want more brains to explode.

You find yourself on Let's Make a Deal, and Wayne Brady picks you to play the famous Three Doors game. The prizes on the line, a million dollars, a goat, and a frying pan.

Being an avid fan, you know how it goes. You'll pick one of the three doors, that door and one of the others will remain closed while the left over door is opened. Wayne asks for your choice and you pick door number 2. So Wayne has them open up door number 1, and its the goat. One mistake avoided.

Now comes the stinger. Wayne asks if you want to keep your choice, or switch to door number 3. So...should you stick it out, or make the switch? What are the odds?

 

[Danalys]

if you don't switch you win a third of the time if you do it's a half.

 

[POWdER-man]

Aw screw it. I want more brains to explode.

You find yourself on Let's Make a Deal, and Wayne Brady picks you to play the famous Three Doors game. The prizes on the line, a million dollars, a goat, and a frying pan.

Being an avid fan, you know how it goes. You'll pick one of the three doors, that door and one of the others will remain closed while the left over door is opened. Wayne asks for your choice and you pick door number 2. So Wayne has them open up door number 1, and its the goat. One mistake avoided.

Now comes the stinger. Wayne asks if you want to keep your choice, or switch to door number 3. So...should you stick it out, or make the switch? What are the odds?

I've never watched Let's Make a Deal so maybe I am missing something but if he picked number two why did they open number one?

 

[Gotham Knight]

I've never watched Let's Make a Deal so maybe I am missing something but if he picked number two why did they open number one?

I've seen the show before. I think that you get to pick one and.....




I'm confused too.

 

[ChillyWilly]

The image you posted proves me right. :cornfused:

#3

I'm not convinced that 2x(3) is any different from 2(3). Given the latest example posted by Bill, however, we can safely say that 2(3) is different from 2x3.

In other words, I think it's something like this:

2(3) = 2x(3) =/= 2x3

Can somebody show that 2(3) is different from 2x(3)? Does the 2 cease to be associated directly with the parentheses when the "x" is added? I'm inclined to say no. I think the problem with the computer calculations isn't that the "x" was added (as you had suggested), but that it doesn't acknowledge the priority of implied multiplication (or that particular form of bracket association) at all.

Aw screw it. I want more brains to explode.

You find yourself on Let's Make a Deal, and Wayne Brady picks you to play the famous Three Doors game. The prizes on the line, a million dollars, a goat, and a frying pan.

Being an avid fan, you know how it goes. You'll pick one of the three doors, that door and one of the others will remain closed while the left over door is opened. Wayne asks for your choice and you pick door number 2. So Wayne has them open up door number 1, and its the goat. One mistake avoided.

Now comes the stinger. Wayne asks if you want to keep your choice, or switch to door number 3. So...should you stick it out, or make the switch? What are the odds?

If you want to explode brains, try picking a problem that isn't presented in high school statistics courses.

if you don't switch you win a third of the time if you do it's a half.

I had heard 2/3 with switching.

 

[Gotham Knight]

And the plot thickens.

 

[ChillyWilly]

I've never watched Let's Make a Deal so maybe I am missing something but if he picked number two why did they open number one?

1) Goat
2) Frying Pan
3) Car


You don't know what is behind each door. Let's say you pick door #2.

Brady will open one of the two doors NOT chosen...whichever one doesn't have the big prize (car, money, etc.) behind it. In this case, he'd open door number one.

This way, you're left with the (closed) door of your initial choosing, and one other closed door (#2 and #3). Of the two closed doors, one has a great prize (#3), and the other conceals a dud (#2). You are then given the option to switch, or stay with your initial choice.

That's the point of the game.

Since you had a 1/3 probability of picking the correct door on the first selection, the probability that the car resides in one of the other two doors is 2/3 (1/3 + 2/3 = 1...check).

This does not change when one of the "dud" doors is opened. That's the key to this problem. You can't simply assume a 50% probability when the one door is eliminated because that disregards the significance of the first choice as if it never happened, when it in fact did happen.

Switching grants you a 2/3 success rate; this becomes clear when several simulations are run in succession. Get a friend and try it yourself...it's actually a pretty fun statistical exercise.

This reasoning also applies to games like Deal or No Deal.

Hint: If on DoND, and you get down to two cases - your own and one other case - SWITCH. The chance that your initial choice contains the million is 1/26. According to the reasoning of problems like the one discussed above, if you DO get down to two cases, and the million is still in play, there's a 25/26 chance that the case NOT in your possession holds the million based on your initial choice.

As with the problem above, the probability isn't simply reduced to 50/50.

Unless I'm mistaken...

 

[Prison Mike]

This thread is making me nervous about my GRE now.

 

[Gotham Knight]

This thread is making me nervous about my GRE now.

 

[Metamorpho1977]

I don't even know what a GRE is.

 

[Danalys]

Unless I'm mistaken...

nope you're not mistaken.

if your first choice is wrong and the only other wrong choice is eliminated then to change is right. so 1/3 becomes 2/3

 

[Ipodman]

Why am I still coming back to this thread...

I've only watched Deal or No Deal... and I always believed that you should NEVER give up as long as the million is still hidden...

 

[Calvin]

I hope I can end this with this example from this page. I post the example below. According to the rules, the answer is one. The author admits that there is always arguing when applying this rule to such problematic equations.

From the article:

This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.

Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
16 ÷ 2[8 – 3(4 – 2)] + 1
= 16 ÷ 2[8 – 3(2)] + 1
= 16 ÷ 2[8 – 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

(graphic on page)

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!

Booyah! I was exactly right from the beginning with the outside/besides parentheses rule!

 

[ChillyWilly]

This thread is making me nervous about my GRE now.

The problems on the GRE are nowhere near as ambiguous as the equation in question (6/2(1+2)). Of course, making sure you have a grasp on the little rules is important. The best thing you can do is get a comprehensive test-prep book and study your ass off!

I recommend the book from the Princeton Review.

 

[Prison Mike]

The problems on the GRE are nowhere near as ambiguous as the equation in question (6/2(1+2)). Of course, making sure you have a grasp on the little rules is important. The best thing you can do is get a comprehensive test-prep book and study your ass off!

I recommend the book from the Princeton Review.

I have the one from Kaplan. So far I'm going through every practice test I can get my hands on.

 

[wiegeabo]

I'm not convinced that 2x(3) is any different from 2(3). Given the latest example posted by Bill, however, we can safely say that 2(3) is different from 2x3.

In other words, I think it's something like this:

2(3) = 2x(3) =/= 2x3

Can somebody show that 2(3) is different from 2x(3)? Does the 2 cease to be associated directly with the parentheses when the "x" is added? I'm inclined to say no. I think the problem with the computer calculations isn't that the "x" was added (as you had suggested), but that it doesn't acknowledge the priority of implied multiplication (or that particular form of bracket association) at all.

If you want to explode brains, try picking a problem that isn't presented in high school statistics courses.


I had heard 2/3 with switching.

Is the x a variable or multiplier? I'm assuming multiplier. If so, it's improper to write it like that. You'd never write something as 2x(something). It would always be 2(something). I guess you could say they're equivalent, but it really should never come up.

 

[wiegeabo]

1) Goat
2) Frying Pan
3) Car


You don't know what is behind each door. Let's say you pick door #2.

Brady will open one of the two doors NOT chosen...whichever one doesn't have the big prize (car, money, etc.) behind it. In this case, he'd open door number one.

This way, you're left with the (closed) door of your initial choosing, and one other closed door (#2 and #3). Of the two closed doors, one has a great prize (#3), and the other conceals a dud (#2). You are then given the option to switch, or stay with your initial choice.

That's the point of the game.

Since you had a 1/3 probability of picking the correct door on the first selection, the probability that the car resides in one of the other two doors is 2/3 (1/3 + 2/3 = 1...check).

This does not change when one of the "dud" doors is opened. That's the key to this problem. You can't simply assume a 50% probability when the one door is eliminated because that disregards the significance of the first choice as if it never happened, when it in fact did happen.

Switching grants you a 2/3 success rate; this becomes clear when several simulations are run in succession. Get a friend and try it yourself...it's actually a pretty fun statistical exercise.

This reasoning also applies to games like Deal or No Deal.

Hint: If on DoND, and you get down to two cases - your own and one other case - SWITCH. The chance that your initial choice contains the million is 1/26. According to the reasoning of problems like the one discussed above, if you DO get down to two cases, and the million is still in play, there's a 25/26 chance that the case NOT in your possession holds the million based on your initial choice.

As with the problem above, the probability isn't simply reduced to 50/50.

Unless I'm mistaken...

That's exactly right. The mistake most people make is they assume that because two doors are left, it's a 50-50 shot. And that would be true if Wayne had opened one of the doors before you got to make your initial guess. Then you'd be choosing out of two. But the probability your initial choice out of three was right doesn't change as the game goes on.

 

[wiegeabo]

If you want to explode brains, try picking a problem that isn't presented in high school statistics courses.

You'd be surprised.

This question was presented to two classes I was in in college. One was a management class, the other an advanced math/computer class.

In both cases, most of the class got it wrong and spent half of the class (and beyond) arguing over it.

I never took high school statistics myself, but I don't remember this coming up in my college stats class. Although, knowing Mr. Adams, he did and I just forgot about it.

 

[ChillyWilly]

Is the x a variable or multiplier? I'm assuming multiplier. If so, it's improper to write it like that. You'd never write something as 2x(something). It would always be 2(something). I guess you could say they're equivalent, but it really should never come up.

It's a matter of interest in this particular debate, though. The solution hinges upon what actually defines a, "parenthetical operation."

Chaseter asserted that the reason the online calculators kept coming up with 9 as the answer was that they added the "x" (multiplication sign). I'm not sure I agree. I think it makes little to no difference, but the fact remains that the calculators seem to disagree with the logic that has led us (generally) to the consensus of 1 as the answer, for whatever reason.

 

[ChillyWilly]

You'd be surprised.

This question was presented to two classes I was in in college. One was a management class, the other an advanced math/computer class.

In both cases, most of the class got it wrong and spent half of the class (and beyond) arguing over it.

I never took high school statistics myself, but I don't remember this coming up in my college stats class. Although, knowing Mr. Adams, he did and I just forgot about it.

I suppose you're right. I remember getting it wrong the first time, too. I understood the reasoning right away upon being corrected, but when presenting the same problem to others, I guess I've encountered similar confusion.

 

[Calvin]

It's a matter of interest in this particular debate, though. The solution hinges upon what actually defines a, "parenthetical operation."

Chaseter asserted that the reason the online calculators kept coming up with 9 as the answer was that they added the "x" (multiplication sign). I'm not sure I agree. I think it makes little to no difference, but the fact remains that the calculators seem to disagree with the logic that has led us (generally) to the consensus of 1 as the answer, for whatever reason.

So what we can all take away from this, is if Skynet ever starts to take over, we just whip out this problem and it'll be screwed.

 

[Metamorpho1977]

I've never watched Let's Make a Deal so maybe I am missing something but if he picked number two why did they open number one?

It's done for dramatic effect.