Wednesday, 7 October 2009

What the... ?!?!?

Okay, so we all know (Derren Brown aside) that the odds of winning the lottery are roughly 1 in 14 million.

What the hell are the odds of this...

At the start of September, the exact same 6 balls were drawn out in 2 consecutuve draws in the Bulgarian lottery.

Sept 6th - 4, 15, 23, 24, 35 and 42

Sept 10th - 4, 15, 23, 24, 35 and 42

I say again... What the ?!?!?!

But how unlikely is this?

Quote from Reuters:
The chance of the same six numbers coming up twice in two consecutive rounds was one in more than 4 million but was not impossible, respected mathematician Michail Konstantinov has said.

Really? Less likely than winning the damn thing in the first place??

Kids immediately destroyed this quote - they know their gambling - and I'm planing on coming at this investigating conditional probability, tree diagrams, extending to see how likely this is if there were 3, 4, 5, 6 balls etc.


One of my students pointed out that the only reason it is surprising is that given that it came out one week, it has become a sequence we recognise, like 1, 2, 3, 4, 5, 6, but it obviously has the same chance of coming out as anything else.

{side discussion from K.- "why would you win less from betting 1, 2, 3, 4, 5, 6 on the lottery compared to pretty much any other set of numbers?"}

This brought to light a mass debate on the nature of randomness - I asked them to stand around the room randomly. Naturally, every kid tried to space themselves evenly from one another. I was non committal when kids asked if they had done it right.

Then we all sat back down, picked our MP3 players / mobiles out and hit random.

For those of us with mighty Sony Walkman, this randomises the order songs play in, but will play all songs through before starting again (admittedly in a different order).

Kids: "Not random"

Some mp3 players did genuinely randomise though (25 did, the rest did not)

Out of a class of 30 plus me (does it say a lot that between us we had 47 devices capable of shuffling music? there's an investigation there i think...)

All these devices on random/shuffle, 1 kid got the same song twice in a row.

We talked about why this could happen (and why we wouldn't want it to happen in an mp3 player) before getting to the idea of random meaning everything having an equal chance of happening - even if it has just happened.

Asked them before they left to stand randomly around the classroom.

Some still spaced themselves out, but some clumped together. Some didn't move at all.

Sincerely - isn't it awesome when a 14 year old can write a better lesson plan than you?

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