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This problem offers an engaging context in which to discuss probability and uncertainty. Intuition can often let us down when working on probability; this problem has been designed to provoke discussions that challenge commonly-held misconceptions. You can read more about it in this article.
Unusual events are expected to happen to someone if the population is large enough. It's impossible to predict in advance who it will happen to, but after the event we shouldn't be surprised that it has occured. This problem provides an example of this phenomenon.
Before the lesson, prepare a sealed envelope with the word FIVE written on it (assuming you have a class of about 30).
There are lots of discussions that can come from this task and from watching the animation at each stage. For example:
The animation could be used with each student choosing a point or region of the grid and seeing if they chose correctly, to capture the idea that the unexpected will happen to someone almost every time, but that it's difficult to predict who it will happen to.
There are some suggested questions at the end of the problem that could be used to explore the ideas further. Alternatively, the class could be asked to think of other examples where very unlikely events happen in very large populations.
What proportion of the people standing do we expect to sit down on each flip of the coin?
Encourage students to start by analysing what happens with only a very small number of people in the room, and to use the interactivity to model it.
Same Number! offers another opportunity to work with probabilities in order to explain unexpected events.
You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?
A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?
A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?