Hi everybody!
It’s Jason again, from Collaborative Mathematics.
This is Challenge 07.
It’s a probability experiment that I first
heard about from a gentleman named Phil Yasskin.
So, thanks for Phil for the tip!
Like I said, this is a probability experiment
so I hope you will try it out for yourself at home,
or at school or wherever you are right now.
I don’t know where you are…
But that you’ll try it, in any case.
What you’ll need is six pieces of string.
So here I have six pieces of yarn that are all about the
same length.
You’ll need your six pieces of string, and a partner.
And…
Here’s my
special effects on Collaborative Mathematics
this time.
So you have your six pieces of string and your partner, and the idea
is that your partner will hold the pieces of string
in their fist, like this, in such a way that you can’t tell
which strings from the top connect to which strings from
the bottom.
So, you might want your partner to do a little probability shuffle,
mix ‘em up a little bit, before they hold them in their fist
like that.
You are going to start tying some knots.
Take two strings that are coming out of the top of your partner’s hand.
Pick to strings at random and tie them together.
I’m going to take these two here and tie them together.
Can you see what I’m doing?
Here we go, tying them into a knot like… so.
So you take two strings and tie them in a knot, and then do it again.
Pick two more strings from the top, tie those in a knot.
Take the last two strings, and tie those in a knot.
Tie them together, right?
So, I’m going to do that. Please hold.
OK. There you go. That’s the first part.
You take these strings that were coming out of the top of your
partner’s hand, in pairs, and you tie them together.
And then… Do you want to guess what
happens next? You’re going to do it down below.
Pick two ends at random, tie them together,
pick two more, tie them together,
and then take the last two and tie those together.
Please hold now while I do that.
OK. There you go. That’s the experiment.
The probability question is: If we do this experiment in this way,
what is the probability that I’ve taken those six pieces of string
that we started with and created one continuous
loop of string, like this?
That’s the question!
Now there’s a couple of ways we might go about approaching this.
We might think about it theoretically, and if there is anybody that has
thoughts about theoretical probability,
I’d love to see some response videos that discuss that.
I’m just as curious to hear about experimental or
empirical results.
So if you try this experiment, then send me your data.
Tell me how many times you tried it and what the outcomes were
each time, and I will start to create some kind of a data table
or a spreadsheet on the website so that we can all look at each others’
empirical data, in addition to maybe thinking about this theoretically.
So you can find me through Facebook or Twitter,
or send me an email.
The links are on the website, somewhere, I don’t know where
I’m pointing to, but they’re on the website.
You can find it.
I hope people will try this experiment and share
their data.
And I look forward to seeing what happens next.
Have fun!