1 00:00:00,680 --> 00:00:01,350 Hi everybody! 2 00:00:01,670 --> 00:00:03,700 It’s Jason again, from Collaborative Mathematics. 3 00:00:03,870 --> 00:00:06,110 This is Challenge 07. 4 00:00:06,530 --> 00:00:09,860 It’s a probability experiment that I first 5 00:00:10,120 --> 00:00:12,630 heard about from a gentleman named Phil Yasskin. 6 00:00:12,870 --> 00:00:15,140 So, thanks for Phil for the tip! 7 00:00:19,220 --> 00:00:21,660 Like I said, this is a probability experiment 8 00:00:21,840 --> 00:00:25,710 so I hope you will try it out for yourself at home, 9 00:00:26,320 --> 00:00:28,330 or at school or wherever you are right now. 10 00:00:28,470 --> 00:00:29,340 I don’t know where you are… 11 00:00:29,770 --> 00:00:31,660 But that you’ll try it, in any case. 12 00:00:32,070 --> 00:00:34,800 What you’ll need is six pieces of string. 13 00:00:35,290 --> 00:00:38,240 So here I have six pieces of yarn that are all about the 14 00:00:38,340 --> 00:00:39,170 same length. 15 00:00:39,790 --> 00:00:42,820 You’ll need your six pieces of string, and a partner. 16 00:00:44,020 --> 00:00:44,690 And… 17 00:00:46,140 --> 00:00:46,960 Here’s my 18 00:00:47,340 --> 00:00:51,000 special effects on Collaborative Mathematics 19 00:00:51,130 --> 00:00:51,590 this time. 20 00:00:52,050 --> 00:00:54,880 So you have your six pieces of string and your partner, and the idea 21 00:00:55,090 --> 00:00:58,290 is that your partner will hold the pieces of string 22 00:00:58,460 --> 00:01:02,250 in their fist, like this, in such a way that you can’t tell 23 00:01:02,470 --> 00:01:05,790 which strings from the top connect to which strings from 24 00:01:05,890 --> 00:01:06,450 the bottom. 25 00:01:06,930 --> 00:01:10,800 So, you might want your partner to do a little probability shuffle, 26 00:01:11,200 --> 00:01:15,210 mix ‘em up a little bit, before they hold them in their fist 27 00:01:15,560 --> 00:01:17,030 like that. 28 00:01:17,520 --> 00:01:19,360 You are going to start tying some knots. 29 00:01:19,570 --> 00:01:23,490 Take two strings that are coming out of the top of your partner’s hand. 30 00:01:23,890 --> 00:01:26,360 Pick to strings at random and tie them together. 31 00:01:29,020 --> 00:01:30,740 I’m going to take these two here and tie them together. 32 00:01:30,970 --> 00:01:32,080 Can you see what I’m doing? 33 00:01:34,070 --> 00:01:37,880 Here we go, tying them into a knot like… so. 34 00:01:38,920 --> 00:01:43,430 So you take two strings and tie them in a knot, and then do it again. 35 00:01:43,700 --> 00:01:46,240 Pick two more strings from the top, tie those in a knot. 36 00:01:46,580 --> 00:01:49,560 Take the last two strings, and tie those in a knot. 37 00:01:49,710 --> 00:01:50,870 Tie them together, right? 38 00:01:51,270 --> 00:01:54,240 So, I’m going to do that. Please hold. 39 00:01:57,370 --> 00:02:00,130 OK. There you go. That’s the first part. 40 00:02:00,290 --> 00:02:05,170 You take these strings that were coming out of the top of your 41 00:02:05,380 --> 00:02:06,380 partner’s hand, in pairs, and you tie them together. 42 00:02:06,800 --> 00:02:08,370 And then… Do you want to guess what 43 00:02:08,590 --> 00:02:10,770 happens next? You’re going to do it down below. 44 00:02:11,020 --> 00:02:16,900 Pick two ends at random, tie them together, 45 00:02:17,160 --> 00:02:18,690 pick two more, tie them together, 46 00:02:19,150 --> 00:02:21,530 and then take the last two and tie those together. 47 00:02:22,350 --> 00:02:24,230 Please hold now while I do that. 48 00:02:28,690 --> 00:02:32,200 OK. There you go. That’s the experiment. 49 00:02:32,470 --> 00:02:36,230 The probability question is: If we do this experiment in this way, 50 00:02:36,610 --> 00:02:41,020 what is the probability that I’ve taken those six pieces of string 51 00:02:41,160 --> 00:02:45,290 that we started with and created one continuous 52 00:02:45,510 --> 00:02:48,740 loop of string, like this? 53 00:02:50,330 --> 00:02:51,290 That’s the question! 54 00:02:51,770 --> 00:02:55,100 Now there’s a couple of ways we might go about approaching this. 55 00:02:55,340 --> 00:02:59,270 We might think about it theoretically, and if there is anybody that has 56 00:02:59,450 --> 00:03:01,690 thoughts about theoretical probability, 57 00:03:01,980 --> 00:03:04,690 I’d love to see some response videos that discuss that. 58 00:03:05,030 --> 00:03:08,870 I’m just as curious to hear about experimental or 59 00:03:09,150 --> 00:03:10,150 empirical results. 60 00:03:10,200 --> 00:03:14,190 So if you try this experiment, then send me your data. 61 00:03:14,470 --> 00:03:17,700 Tell me how many times you tried it and what the outcomes were 62 00:03:17,850 --> 00:03:22,080 each time, and I will start to create some kind of a data table 63 00:03:22,300 --> 00:03:25,740 or a spreadsheet on the website so that we can all look at each others’ 64 00:03:26,010 --> 00:03:31,030 empirical data, in addition to maybe thinking about this theoretically. 65 00:03:31,200 --> 00:03:35,920 So you can find me through Facebook or Twitter, 66 00:03:36,150 --> 00:03:37,440 or send me an email. 67 00:03:37,800 --> 00:03:40,740 The links are on the website, somewhere, I don’t know where 68 00:03:40,920 --> 00:03:42,660 I’m pointing to, but they’re on the website. 69 00:03:42,990 --> 00:03:43,440 You can find it. 70 00:03:43,850 --> 00:03:48,560 I hope people will try this experiment and share 71 00:03:48,760 --> 00:03:49,330 their data. 72 00:03:49,650 --> 00:03:51,660 And I look forward to seeing what happens next. 73 00:03:51,880 --> 00:03:52,380 Have fun!