During a garden party, there is a lucky draw where a number of envelopes containing a card are placed in a drum. Printed on the card is the amount of money you win by selecting that particular envelope. You are able to win 5 RMB, 10 RMB, 20 RMB, 50 RMB or 100 RMB. The total value of all the cards which read “You win 5 RMB” is 500 RMB; the total value of the card which read “You win 10 RMB” is 500 RMB and so on until you would guess that the total value of all the cards which read “You win 100 RMB” is also 500 RMB. Once you select your envelope, your prize is revealed and you are given the appropriate amount of money.
The card is then placed back in the envelope and returned to the drum after each play. Since the envelope containing the card is returned to the drum, the chances of winning any particular amount remains the same.
It costs 15 RMB to play the game. If you randomly choose one of the envelopes from the drum, what is the probability that you win more than you paid to participate in the game?
This is one of those problems where some simple KS3 mathematics might not be enough and some jottings on a piece of paper will be of great help!
As always, you can submit your ideas and answers to me here.
Martin Brown, Head of Mathematics