Let's focus now on a technique that is used at football matches to decide which of the two teams should kickoff.

As you already know, a coined is tossed and each team chooses one of the possible outcomes: heads (c) or tails (+).

a) Use Laplace's rule to work out the following probabilities: p(c)=      p(+)=

b) Toss one coin 50 times (which is the same as tossing 10 coins 5 times each) and write down the number of times you get heads. Carry out this experiment in the window below.

Each time you increase the number of throws you should count the number of heads. Each 'throw' includes 10 coins which is the same as tossing one coin 10 times. If you want to know how many heads you would get after tossing the coin 50 times you just have to toss the coins in the window above 5 times and make a note of the results.

c) Copy a table like the one below into your exercise book, count the number of times you got heads and record the number in the table.

d) Plot the cumulative number of throws (on the X-axis) and the relative frequency (on the Y-axis) on the graph in the following window.

You should have noticed that the relative frequency (the probability of getting heads when you toss a coin) is very close to 0.5 and gets closer the more times the coin is tossed.

Use the mouse to move the red points to the positions you got in the table above.

The above can be summarised in the following conclusion:

In a random experiment the relative frequency of an event gets closer and closer to its theoretical probability as the number of times the experiment is carried out increases.

This is known as the Law of Chance or the Law of Large Numbers.