Expected Value in Betting Games

What does an expected value of -$0.56 in a betting game imply?

A) Carlie will win $0.56 every time she plays the game.

B) Carlie will lose $0.56 every time she plays the game.

C) If Carlie plays the game many times, on average, Carlie should expect to lose about $0.56 each game.

Answer:

The correct answer is B) Carlie will lose $0.56 every time she plays the game.

The concept of expected value, in the context of betting games, is an average outcome if an experiment (like a bet) is repeated many times. Carlie's expected value of -$0.56 per game means she should expect to lose an average of $0.56 over many games.

Explanation:

The concept being discussed here is expected value in probability, specifically in the context of betting games. Expected value gives us an average outcome if an experiment (like a bet) is repeated many times. In Carlie's case, an expected value of -$0.56 for each bet means that option C is accurate. If Carlie plays the game many times, on average, she should expect to lose about $0.56 each game.

This does not mean she will lose exactly $0.56 each time she plays, but rather it's the average loss per game when considered over a large number of games. Therefore, the correct answer is B) Carlie will lose $0.56 every time she plays the game.