Question 1162234: Your friend offers you to play a game. To play it, you will roll two fair dice. If the sum of the two numbers obtained is 2,3,4,9,10,11,or 12, you will win RM20. However, if the sum of the two numbers is 5,6,7 or 8, you will pay your friend RM20. From this game, you observe that you have seven winning numbers and only four losing numbers. Should you play this game? To decide, provide appropriate calculations to support your reasons.
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
"Should you play this game?" is not a question that can be answered by mathematics. You should play it if you feel lucky, and if you don't mind paying your friend the RM20.
If you play the game multiple times, your expected winnings are negative; in that sense the game favors your friend, so you should not play.
P(win) = P(2 OR 3 OR 4 OR 9 OR 10 OR 11 OR 12) = 1/36+2/36+3/36+4/36+3/36+2/36+1/36 = 16/36 = 4/9
So for playing the game a large number of times, the expected value of your winnings is
(4/9)(20)+(5/9)(-20) = -20/9
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