OK class, time for MATH!

[RickyZ]

I saw this in a math text and wanted to see what you thought...


You have 3 quarters. You toss them in the air and let them fall to the ground. What are the chances they will land with 2 heads and 1 tail showing?

 

[DuchessAimee]

How do you toss them into the air?

Is it inside or outside?

Do I toss them one at a time?

Are they pre 1967 quarters?

Are there people watching me?

Does anyone's life depend on this outcome?


I have a lot of questions, Rick.

 

[kenisyes]

I am a math professor currently teaching the class in which this is taught. I have voted for the correct answer. You now have a one in two chance of picking the right answer, as someome has posted the wrong answer, and only two have voted. There is exactly one person at CC, besides me, who can now determine the right answer (the one who posted the wrong answer), and know it is right.

What are the odds of choosing the correct religion, if you are brought up with none? That's a better question.

 

[SpudLove]

hand up I got it wrong

 

[didymos]

Sadly, we don't use quarters anymore....

I got it right though.

 

[RickyZ]

My view is there are only 4 ways they can land - all heads, all tails, two heads, and two tails. Ergo it's one in 4. The text splits it down to individual quarters:

HHH
HHT
HTH
THH
TTH
THT
HTT
TTT

It reasons that there are 3 out of the 8 landings which produce a 2-head response. But those 3 (HHT, HTH, THH) are all the same answer, so those 3 only count as 1 result. It's like saying 1+2+3 and 2+3+1 and 3+1+2 are three different equations, but they're not. They all produce the same result, so they are just 3 different ways of stating the same single equation. And the question wasn't how many ways can you state the result, it asks what is the overall end result? And the end result is there's only 4 different ways they can land.

?

 

[T_Laurich]

My view is there are only 4 ways they can land - all heads, all tails, two heads, and two tails. Ergo it's one in 4. The text splits it down to individual quarters:

HHH
HHT
HTH
THH
TTH
THT
HTT
TTT

It reasons that there are 3 out of the 8 landings which produce a 2-head response. But those 3 (HHT, HTH, THH) are all the same answer, so those 3 only count as 1 result. It's like saying 1+2+3 and 2+3+1 and 3+1+2 are three different equations, but they're not. They all produce the same result, so they are just 3 different ways of stating the same single equation. And the question wasn't how many ways can you state the result, it asks what is the overall end result? And the end result is there's only 4 different ways they can land.

?

But lets not forget if all the quarters are heads up then what you get is HHH... And the probability of the first quarter landing is 1/2. The next quarter is also heads up 1/2. and the third is also 1/2... Now you multiply the events I forget why you do. I just remember a math problem involving cards and it was around the same premises...

So you get 1/2 x 1/2 x 1/2= 1/8.... Which the correct answer and method for HHH

But when you use the same method for HHT you still get 1/8...


I hope I cunfuzzled you

 

[wwjd_kilden]

*runs away from the math*

I never understood probability, all I know is this:
If people are asked to fake randomness, they make it TOO random, thus obvious.

 

[T_Laurich]

*runs away from the math*

I never understood probability, all I know is this:
If people are asked to fake randomness, they make it TOO random, thus obvious.

I heard a story recently that Statisticians say that they can have ten rooms flip a coin 10 times and write the results on the board. Then have 1 room make up their answers. And every time they could tell exactly which room did not flip the coin. Because in the real world a coin could flip 8 times and get heads. But a human would never think that was believable and thus never put an 'absurd' answer...

 

[kenisyes]

And the question wasn't how many ways can you state the result, it asks what is the overall end result?

The question is "What are the chances they will land with 2 heads and 1 tail showing?". "Chances" is based on the technical term "probability", which is defined as "successful outcomes (in this case two heads) divided by total possible outcomes". The chart shows 3 outcomes with two heads, out of 8.

Personally, if I wanted to argue, I'd spend my time in a thread about tongues or the virtues of Catholicism.

 

[Blain]

I am horrible at math but was leaning towards something else. So what is the correct answer?

 

[Mammachickadee]

so what's the correct answer?

 

[MaranathaSoonQuick]

Doing this with 3 quarters all facing heads up, I got 4 out of 8 so that's ½ for me, this was out of one test though, so results may vary.

 

[RickyZ]

The question is "What are the chances they will land with 2 heads and 1 tail showing?". "Chances" is based on the technical term "probability", which is defined as "successful outcomes (in this case two heads) divided by total possible outcomes". The chart shows 3 outcomes with two heads, out of 8.

Personally, if I wanted to argue, I'd spend my time in a thread about tongues or the virtues of Catholicism.

I'm not looking to argue, just to understand. And there's already a ton of threads on tongues and Catholicism. Sometimes it's nice to step back from the firing line and take a break with something else. A momentary diversion, as it were.


But this also applies, somewhat, to scripture interpretation. How do you look at things? Someone who sticks to a strict analytical book knowlege would answer 3/8 based on the "HHT" charting. Someone who lives a more street-functional existence will answer 1/4 because, as they lay on the floor, HHT, HTH, and THH are functionally all one and the same result. 2 heads and 1 tail. Applied to, say, tongues, a book analyst might just find them dead. But a guy in the trenches, looking more at the overall results than the critical analysis, will find that they're alive and well. And isn't that somewhat what we find here on the tongue threads? The bookworms are against it, the worker bees are for it. In general that is.

Does that make any sense and make it more appropriate for discussion?

It would be interesting to take 3 quarters and toss them 100 times, logging the overall results, and see what that trial shows.

On a related note, I found these interesting tidbits: according to a university study, a coin flipped will land showing the side that was originally up 51% of the time. And a coin spun on it's edge will land tails up 80% of the time, because the head side is slightly heavier.

And I have flipped a quarter and seen it land on it's edge. How does that figure into the equation?


OK, enough diversion. What thread is Zone on?

 

[RickyZ]

And then it clicks. Wow, it is amazing, the human ability to stare right at something and not see it.

1 out of 4 would be the correct answer if the question was 'in how many ways can they land?' Yes there are four ways in which they can land. But for 2 of those ways, there are 3 ways to achieve that. That's what bumps the chances from 1/4 to 3/8. Duh.

I knew I was missing something. Determined to hunt it down and there it is, the missing link. Thanks for helping, guys.

And oh yeah, the answer is 3 out of 8.

What grade do you teach Ken? Maybe I need to sit in. lol

 

[kenisyes]

I'm not looking to argue, just to understand. And there's already a ton of threads on tongues and Catholicism. Sometimes it's nice to step back from the firing line and take a break with something else. A momentary diversion, as it were.


But this also applies, somewhat, to scripture interpretation. How do you look at things? Someone who sticks to a strict analytical book knowlege would answer 3/8 based on the "HHT" charting. Someone who lives a more street-functional existence will answer 1/4 because, as they lay on the floor, HHT, HTH, and THH are functionally all one and the same result. 2 heads and 1 tail. Applied to, say, tongues, a book analyst might just find them dead. But a guy in the trenches, looking more at the overall results than the critical analysis, will find that they're alive and well. And isn't that somewhat what we find here on the tongue threads? The bookworms are against it, the worker bees are for it. In general that is.

Does that make any sense and make it more appropriate for discussion?

It would be interesting to take 3 quarters and toss them 100 times, logging the overall results, and see what that trial shows.

On a related note, I found these interesting tidbits: according to a university study, a coin flipped will land showing the side that was originally up 51% of the time. And a coin spun on it's edge will land tails up 80% of the time, because the head side is slightly heavier.

And I have flipped a quarter and seen it land on it's edge. How does that figure into the equation?


OK, enough diversion. What thread is Zone on?

You should be in my class. I'd give you 40 points for two week's worth of great comments.

I do not believe you are looking to argue, but I thought some others might be. That response was directed at them.

An experiment is a really good idea. I suggest you try it and let us know. You will get around 35 or 40 times, not 25 or so. More precisely the standard deviation is square root of 100 times 3/8 times 5/8, or just under 5. So 95% of the time you try the hundred times, you should get 3 heads between 28 and 47 times. If the correct answer were 1/4, these values become 17 and 33. So an experiment or two will help you separate the two answers.

The 51% can be allowed for, as can the landing on the side, but you don't want to see the equation! The question in a math textbook will say farther up the page that the coin is a "fair" coin, meaning it is not heavier on one side. I usually propose to my class that fair coins do not exist, and that all our computations are at least a little wrong just because life is not fair.

You are correct, that how we approach it betrays our personality. Street smart, by the rules, ouside the box (DutchessAimee post #2), or just running away from math.

I would enjoy the diversion more if I were not teaching two classes right now.

 

[reject-tech]

1 and 3 which equal 4 are both "odds"
3 and 5 which equal 8 are both "odds"
lol

 

[jb800m]

math is always fun!!!!!!!

 

[RedTent]

I love this. I use the probability of things all the time. Is it saver to drive or fly? Can I go to the concert in down town alone, being I would have to take an expensive taxi or take a chance on the dangers of downtown at night? What are the dangers of downtown at night, is it worth it to take the chance? Organic food at it's expense or take a chance on non organic? What are the probabilities?

Back when eBay had real buys, I saved hundreds of dollars by buying there. I was once cheated. I was still way ahead. My friend would only buy from a place that guaranteed so her money did not go nearly as far as mine but she was never cheated. She was unable to comprehend probabilities, so she wasn't able to see that she was buying safety and paying dearly for it. She was buying something (safety), but she was unable to know how much what she was buying cost in actual dollars because she hadn't learned about probabilities.

 

[RickyZ]

1 and 3 which equal 4 are both "odds"
3 and 5 which equal 8 are both "odds"
lol

Two odds will always equal an even

Two evens will always equal an even

Isn't that odd?