We are going to play a game of chance. We will roll a die (half of a pair of dic
ID: 3075345 • Letter: W
Question
We are going to play a game of chance. We will roll a die (half of a pair of dice) and if it comes up with one or two spots showing, you win and I will pay you $1.50. If it comes up with three, four, five, or six spots showing, you lose and you will pay me $1.00. So, the probability that you will win is 1/3 and the probability you will lose is 2/3. What is the expected value of this game for you? (show calculations) Would you want to play this game? Why? If we played the game 100 times, about how much would you expect to win or lose in total?
Explanation / Answer
The probability of winning is 1/3.
The probability of losing is 2/3.
That is P(x=1.5)=1/3
P(x=-1)=2/3
Expexted value=1.5*1/3 - 1*2/3=-1/6
Expected value is losing $0.167.
You shouldn't play this game as a loss is expected.
If we play 100 times expected loss=100*1/6=$16.67
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