Respuesta :
Hello there. To solve this question, we need to analyze the probabilities for each case and see if the game is fair or not and also favorable to the player.
Sophia rolls a dice. If 5 turns up, she gets $2; If 6 turns up, she gets $3; If 2 turns up, she loses $10; She neither wins nor loses if any other face turns up.
First, let's remember something that will be important: a dice only haves 6 faces.
As we can see, she is winning (getting money) if 2 out of 6 faces turns up (5 and 6), and is losing if 1 out of 6 faces turns up (2). She is neither winning or losing if 3 out of 6 faces turns up (1, 3, 4).
About the fairness of the game, there are only 1 case she loses and 2 cases she wins something. We could only say the game is fair if the amount of winning cases were equal to the amount of losing cases. The game is not fair.
About being favorable, we'll consider it being unfavorable just the case that she loses money. The first and third cases, in which she gets money or doesn't get or lose money are favorable to her.
Since only 1 out of 6 faces makes her lose, then the game is favorable to the player.
Final answer: The game is not fair, but favorable to the player.
