Jennifer is playing a game. The game involves choosing a series of boxes to open with the final outcomes of win (earning one point), lose (earning zero point) or draw (setting with a half point).
The game begins with Jennifer choosing either red box or blue box. If Jennifer chooses the red box, there are 60% chance that a smaller pink box is inside of the red box. There are 10% chance that the pink box contains just a black stone. If it is black stone, Jennifer loses the game. However, there are 90% chance that the pink box contains another grey box. If it is a grey box, Jennifer will be given an option to settle the game as draw without opening the grey box. If Jennifer chooses to open the grey box, however, there are 80% chance that the grey box contains a white stone (which means Jennifer wins the game). On the other hand, there are 20% chance that the grey box contains a black stone (which means Jennifer loses the game).
At the same time, there are 40% chance that the red box contains a purple box. Jennifer must open the purple box. The purple box has 70% chance of containing a white stone (win) and 30% chance of containing a black stone (lose).
If Jennifer chooses a blue box at the beginning, on the other hand, there are equal chances that the blue box contains either a green box or a navy coloured box. For both green box and navy coloured box, Jennifer is given an option to settle the game as draw without opening the box. If it is a green box and Jennifer chooses to open the box, there are 20% chance of green box containing a white stone (win) and 80% chance of containing a black stone (lose). If it is a navy coloured box and Jennifer chooses to open the box, there are 40% chance of the navy coloured box containing a white stone (win) and 60% chance of containing a black stone (lose).
Develop a decision tree to represent Jennifer’s game.
Then answer the following questions:
• Discuss whether Jennifer should choose the red box or the blue box if Jennifer is making decision based on expected value outcome.
• Discuss whether your answer will change if Jennifer must have the outcome of “at least a draw”