Experimental probability

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

Is the regularity shown in this encoded message noise or structure?

Can you work out which spinners were used to generate the frequency charts?

Can you decide whether these short statistical statements are always, sometimes or never true?

When two closely matched teams play each other, what is the most likely result?

Are these domino games fair? Can you explain why or why not?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Can you work out the probability of winning the Mathsland National Lottery?

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?