Consider the following scenario when answering the following questions:
Ivett and Desiree are considering playing a game called Twenties versus Fifties.In this game,Ivett will place a $20 bill on the table,and Desiree will place a $50 bill on the table.Both players will then toss a fair coin.If both Ivett and Desiree toss heads or if they both toss tails,Ivett wins the $70 on the table.If one woman tosses heads and the other tosses tails,Desiree wins the $70 on the table.
-Which of the following is the formula that Desiree would use to compute the expected value (EV )of the game from her perspective?
A) EV = 0.5 * ($20)+ 0.5 * ($50)
B) EV = 0.5 * (-$20)+ 0.5 * ($50)
C) EV = 0.5 *($20)+ 0.5 *(-$50)
D) EV =0.5* (-$70)+ 0.5 * ($50)
E) EV = 0.5 *($70)+ 0.5 * ($50)

Question

Quizplus · Accepted Answer

Desiree's expected value (EV) will be the sum of the product of her probability of winning and the respective payout, for each possible outcome.

In this game, there are four possible outcomes with an equal probability of 0.5 each:
1) Ivett and Desiree both toss heads
2) Ivett and Desiree both toss tails
3) Ivett tosses heads and Desiree tosses tails
4) Ivett tosses tails and Desiree tosses heads

Desiree's payout depends on the outcome of the coin toss, as explained in the scenario. She wins $70 if Ivett and she get the same result and $50 if they get different results.

Therefore, Desiree's EV can be calculated as: 
EV = (0.5 x $70) + (0.5 x $50) 
EV = $35 + $25 
EV = $60

Option C correctly represents this calculation: 
EV = 0.5 x ($20 + $50) + 0.5 x ($20 - $50) 
EV = $35 + (-$15) 
EV = $60

Consider the Following Scenario When Answering the Following Questions