Question

You pay $10 to play the following game of chance. There is a bag containing 12 balls, five are red, three are green and the rest are yellow. You are to draw one ball from the bag. You will win $14 if you draw a red ball and you will win $12 is you draw a yellow ball. You win nothing if you draw a green ball. Is this a fair game? Why or why not?

Answer 1

Since the expected value of the game ($9.83) is less than the cost to play ($10), it is not a fair game because, on average, you would lose money over time.