Alex designs a game for people to play, using two fair five-sided spinners. A person wins the game when both spinners land on the same letter. People pay 40p for each game they play. The prize for a win in £1. Is she likely to raise money?

In order to raise money, we need the average number of wins to be smaller than the average number of losses by at least a factor of 0.4.
The average number of wins will be the number of games multiplied by the probability of winning.The average number of losses will be the number of games multiplied by the probability of losing.
Therefore the probability of winning must be less than 0.4 in order for Alex to raise money.
the probability of winning is simply 1/5, or 0.2.This can be thought of intuitively or formally shown using a probability space of 25 equally likely possibilities, 5 of which will be instances of matching scores.
The probability of winning is less than 0.4 so Alex will gain money on average.