The squares show a 10x10 design for a ‘roll a coin’ board at a local fair. Thedesign is repeated throughout the board. The squares are each of length 5 cm andthe only coins used are 2 cents of diameter 2.5 cm. Show that the probability that a coin of this diameter will soon come to rest nottouching the side of a square is 0.25.Coins are rolled on to the board and a prize is won if the coin comes to rest nottouching a line. The prize is either the amount, in cents, written on the squareor, if the square is blank, the coin is returned. Coins which come to rest on a lineare losers.Would this game make a profit or a loss and what fraction of the takings could beexpected to be given out as prizes?Make a 10x10 design for a ‘roll a coin’ board so that all the takings can beexpected to be given back as prizes, using at least one of each of 50c, 20c, 10c and 5c squares.
I don't understand how to show the probability as 0.25 and how the length of the squares affect it. I'm guessing that it is less likely that you would get a prize since there are more squares that are blank... Are there more than one possibility to make the design?