All entries for Friday 01 October 2010
October 01, 2010
I’m writing this on Saturday morning because when I got home last night I was in no fit state for blogging!
On Friday morning we were forced to move to the lecture theatre because with the GTP students visiting, our usual room wasn’t big enough. I hated this. Despite Peter J-W giving a really interesting presentation about something I really like thinking about, I couldn’t concentrate and found myself switching off. Lecture theatres bring back bad memories for me, of sitting facing the board for an hour whilst the lecturer talks about something I don’t understand and can’t follow (and with my eyesight as it is, could barely even read). But my lecture notes were always very neatly written. That’s what counts, right?
Anyway, so we were doing about probability. We started by discussing randomness, and what that means. We were asked to discuss with the person next to us and finish the sentence: randomness is…
Here’s what me and Chris came up with (I have omitted the particularly silly answers so I don’t get told off for not taking the exercise seriously):
Randomness is unpredictable
Randomness is predictable
Randomness is what makes life interesting
Randomness is an illusion
Randomness is something that has no pattern
Then we looked at two interesting probability problems. DO NOT READ THE ANSWERS UNTIL YOU’VE HAD A GO YOURSELF that includes you, English-with-drama trainees if you’re reading this!
Interesting problem Number 1:
I have 4 counters in my pocket, two red and two green. I take one out without looking at it, and hide it under a book on my desk. I take out another counter, and find that it is green. What’s the probability the counter under the book is green?
Common Incorrect Solution:
½. When you take the first counter out of the bag, the probability of it being green is ½. Surely whatever you do after that can’t change this?
Why this is wrong:
Imagine there were just two counters in your pocket, one red and one green. You take one out and hide it. The probability it’s green is ½. Then you take the other counter out and look at it. It’s red. Then surely the probability the other one is green has to be 0? Conditional probability means that the probability of events can change when we learn new information.
1/3. So you’ve just picked out a green. The probability that you pick out a green is 1/3 if there are two reds and one green (and hence a green under the book) and 2/3 if there are two greens and one red (with a red under the book). So given that the counter is green, it is two times more likely that the counter under the book is red. So the probability it is green is 1/3.
Interesting Problem Number 2:
I have a hat containing three cards. One is blue on both sides, one is green on both sides, and one is green on one side and blue on the other. You pick out a card and lay it on the table. The side you can see is blue. What is the probability the other side is also blue?
Common Incorrect Solution:
½. The card on the table can’t be the green-on-both-sides card, so it is either the blue-blue or the blue-green card. So in one case out of two, the other side is blue, and in the other case it is green. So the probability of it being blue is ½.
Why this is wrong:
The people who say ½ are not considering the faces of the cards, just the cards themselves. See below for more details.
2/3. When I first saw the problem I saw straight away it was 2/3 by reasoning like this: you’ve picked a card and randomly chosen one of its sides. If it was the blue-green card, the probability the blue side is facing up is ½, and if you’d chosen the blue-blue card, the probability would be 1. So given that you’ve put it down and you can see a blue side, you are two times more likely to have picked the blue-blue card than the blue-green card. So the probability the other side is blue is 2/3, and green 1/3.
Johnny had a better way to explain it: In the hat we can represent the three cards like this: G1G2, B1B2, and GB. We take out a card and put it down. The side we can see is blue, so the possibilities are: B1 face up & B2 face down, B2 face up & B1 face down, B face up and G face down. So looking at the face down colours, there are two blues and one green, so the probability it is blue is 2/3.
One good thing about being in the lecture theatre instead of our normal room is that we got to sit with people who are not the people in our usual groups. Now I absolutely adore my group (go team Hopper!) but it does make a nice change to discuss things with other people for once, and because I also adore some people who aren’t in my group (you know who you are!)
We then split the whole group in half and went into separate classrooms. Thankfully my group were going to our usual classroom. We talked a bit more about the problems above, and read a bit about other misconceptions in probability, including: equiprobability (thinking everything is equally likely), the outcome approach (probabilities are based on the strength of causal relationships), the conjunction fallacy, insensitivity to sample size, and local representativeness (expecting the outcomes to reflect the sample space).
After lunch the GTPs had gone home so we were all back together in one room. Andrea took us for the rest of the day. We read a bit more about statistics (where’s the P in statistics?) and then had an activity to do. We had to make paper helicopters based on a design we’d been given. The idea was to try and make the best helicopter by varying the type of paper, length of wings, etc. I didn’t really engage in this task, I think it was a bit two boyish for me. The normally very calm and laid-back Naresh was very excited about this task, and was the first to get cutting and sticking. We didn’t really come up with a plan beforehand, everyone just started making helicopters. Then we tested them by throwing them off the balcony. They picked the best two, and set about modifying them. Sticking a pound to the tail of the helicopters makes them fall very fast, but you don’t get that nice twirly action. So I’m not sure which helicopter was the best, it depends what you want from your helicopter, really. If I’d been judging, I would have said the best helicopter was the most beautifully decorated one (extra points for glitter) but that’s just me.
The idea of the exercise was to practise collecting and recording data. The idea is that if your activity has a purpose, you engage with it more and hence learn better. The purpose in this case was to build the best helicopter.
After that we had to design our own activity. Details of this can be found on Giulian’s blog
I was very very very tired by about 3pm today, and lost my focus a lot. However, I perked up when we finished at 4:30 because some of us were going to the pub! We got to Varsity at 4:45 but it was still closed! It opened at 5pm and we were the first people to be served in the brand new and improved Varsity, which looks very nice now. There were loads of us, about 12 probably. Some people were talking about educational issues, some were playing Testament Trumps, and some of us were talking about… erm, other stuff. Much enjoyment was had by all, and I feel really lucky to have met such wonderful people and to have made so many friends in my first two weeks. I love you all!
Emma x x x